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19 (... )!'! '!* $$% "# (.. P )!/# ( P!* V, = 1, )!'/' -':.) a a = a + a, = 1, n, (.3) ( a a ) a ( a a ), (.4) 1 -.!*., a. "( V. * M(s) N(s) ) )!, )!' )' ), '" ) #. ) ' #.!. )!' # )( ) γ M ( s) + (1 γ ) N( s),.) γ 1. )!!)/1' [5]: * ") (.. P..) )!' # (!, ").. P #) )( (*. #!. &' " #. "!' $$ '* #/ (*,! (! )! $$%! ()( * #

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23 3 '! (.1). )!'!('!* )! - #*,!( "!* ) (.1) -' (.3) n P( s) + a s =. (.5) = (.5) " #-' #!* R P( s) + a s =. (.6) * (.6) '!'' ( )( # '"*/..) )(' $%'! " )!' # #) * ) W as ( a, s) = (.7) P( s) +!"' (.6) (.7) "%..).$, ", ( " a! (.3) )-'!/ $% (.7), /1 ) % ). %.).$..) )!' R, ' (.6) R. #"/ $.. φ S #) )! -': φ ( R ) = RS, : P φ ( V ) = U.!)!*,.! # #!!!"% (.1), #D) '!'' # ' S, #).( RS )(!*.).$. ) "!' * S.(!*.).$. (.1) " #-'!. G j '!*.( j as a js P s ( ). + + = (.8)

24 4 * ) " ' (.8) ) s = α + jβ, r 1, n. )!'' (.8) ) s r )!'' 1/ / (,!( )! )' a a j : j a Re( α + jβ ) + a j Re( α + jβ ) + k p + Re ak ( α + jβ ) + ap( α + jβ ) = ; k p j a I( α + jβ ) + a j I( α + jβ ) + k p + I ak ( α + jβ ) + ap( α + jβ ) =. k p &!' (.9)!)/1 )!('. r (.9) 1. ' " ) a = a, a j = a.!)!*, P G j. j φ 1 ( s ) = P,.) P = ( a, a ), ( r. '!(/' ' -!. ".!), (! G j 1 #' '' t ( ), '!/# " (.9), ( φ 1 ( s ) = t. r j 1.6 #-. (... # '

25 5 (' # #. #-'.% #! S r!!"%. '! s r, * φ 1 ( s ) = P, ( r 1 ( ) φ S = G (.1) r P R j.. ) P '!'/' ) (.9), (" RS )' *, )'1' s r.!)!*,! (.1).% /1' #" # G j. S r '!'/' * φ 1 ( sr ) = t t G j = PP 1 (( P 1 P )!- # G j ).!)!*, PP 1 φ ( ) = sr (" s r (". # "! #"( U ) ) -.).$!* $$%, #"/1 ' t #..! ) -) U..).$.! ) /1' U!- -) )' /1' - # '.!)!*,!(! (.1).% S r )' /1' #" ) # #", G j. RS. )*.% #!!!"% ' (.1) %!, ((, '* U. " #.( (#"( GRS ), #".( # ( GR ), #", )!-1 GR,.( "! ( GU ). 1.7 ) #-' (... '!*!/!*. 1.7 " #!* S r,.% '!'/' /1' #" # 1.7#.( /1' #" # P. P,

26 6 ) #) 1.7 #"'.% #!!!"% -, (!*. (.! P 1 ) # GR )!' #!!!"%!. * φ ( V ) = s1, s1 = α1 + jβ1, φ ( V ) = s, 1 ( ) s φ S1 = P, = α + jβ, ( s 1 '!''.( )!' S 1 s )!' S φ 1 ( S ) = P. &, ( ) "!* $$% a " " V ) " /.%, )!'/!' (.3) (.4). "!* - "*', ( s 1 S 1, s S.!( φ 1 ( s ) 1 P, φ 1 ( s ) P, (

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28 ( j ) ( j ) 8 ( j j ) ( j j ) Re ( α + β ) Re ( α + β ) = = I ( α + β ) I ( α + β ) ( α + β ) + p ( α + β ) Re ak ( j ) a ( j ) k p = I ak ( j ) a ( j ) k p k p ( α + β ) + p ( α + β ) k p. (.11) (), ( α β )!- '!'*' '!( " (.11)! j j Re (( α + jβ ) ) I (( α + jβ ) ) Re (( α + jβ ) ) I (( α + jβ ) ) = ; j k p Re (( α + jβ ) ) I ak (( α + jβ ) ) + ap (( α + jβ ) ) k p j k p I (( α + jβ ) ) Re ak (( α + jβ ) ) + ap (( α + jβ ) ) =. k p (.1) 3, ( )!' (.! S r!./'!!! "- "! U / ) α < β. "!*!" (.1)!(!)/1 -). '1#. "! U (' # 1/!* #-'!., #" $$%! (.1) ), )!'/1!/ j 3. (.13) "&%'+('. )! (.1) #/ ) α + jβ = s. $!.( )! #" (.1) ) b b s = s (cos( bϕ ) + jsn( bϕ )) + j s (cos( ϕ )sn( jϕ ) cos( jϕ )sn( ϕ )) = ; j+ z az s (cos( jϕ )sn( zϕ ) cos( zϕ )sn( jϕ )) =, z (.14)

29 .) z = k p. (.14) ) U * '!'/'.! φ )!* s. (', ( α, β, -!*"' "..( $%, ' (.14) - * 9 sn(( j ) ϕ) = ; j+ z az s sn(( z j) ϕ) =. z (.15) (), (!-!' α < β ' (.15) )!- )!'* ϕ, ϕ 9.!( (.15) #) * '!* j 3. ; ' )!'!! )!'/' - π ϕ = π, j = 3,4,5... j ) "(' ϕ (.15) "!' )!* s,,, )!* ) U!!. #", #)! U S '!''!( (.1)!* $$% ), )!'/1 (.13). r 1.3. )! #-' P )!'!(' $$ )!,.)!* '!'/'!* ($"(),! )'1 $$% (.!. * (! ): = ( ) ( ) D( s) = T A ( s) + B s =, T T T, (.16)

30 3 k k j j.) A ( s) = ( a, js ), B( s) = ( bjs ). j= : j= &!' #-' φ P S!*"!)/1 -: k ( ) D ( s) + T A ( s) =, (.17) =.) D ( s )! "('!*, /1 (.... # P #)!*"* ) #"( R,.) ), = 1,, ) V, " T # '' T. (.17) " #-' # R!/!* : ( ) ( ) D s + T A s = (.18) - (.7) )!'!(' $$ )! #) * ): " W ( T, s) D A ( s) ( s) T = (.19) T (.18), '*!/ $% (.19)!', #"/ )(!*.).$. /#'.* )!* T P '!'' '.!*! "' (.16) " #-'!. T j " ) V. ( ) ( ) ( ) j j G j : D s + T A s + T A s = (.) * sr = α + jβ, r 1, n. )!'' (.) ) s r,!( )! )' T T j : ( ) ( ( )) ( ( α β )) ( ( α β )) ( ( )) ( ( α β )) ( α β ) T Re A + j + Tj Re Aj + j + Re D s = ; T I A + j + Tj I Aj + j + I D s =. (.1)

31 31 &!' (.1), )!'!('!* )! $$%!, - )!(': T = T, * 1. T j = T.!)!*, * j )!-! G j. 1 * φ * * * ( sr ) = P, P ( T, Tj ) =, ( (.. ".!), (! G j 1 '' t, '!/# " 1 (.1), ( ϕ ( s r ) = t.!. #- P!(!* )! #- # * P P )!'! $$ )!*/ - )"*, ( #. - )*.%!*/, ((, '* )!!!(' * U. * U. #! ",! '!''! ' "* (1.8). ; "*,! 1/ α β, (!'/' : ( ) ( ) ( ) ( ) ( D ( α + jβ )) ( ) Re A Re Re α + jβ A α + jβ = = I A α + jβ I A α + jβ I D α + jβ ( ) (.) &!' #) *!(/ " (.) )! : ( ) ( j α β ) ( ( α β )) ( Aj ( α jβ )) I( D ( α jβ )) ( Aj ( α jβ )) D ( α jβ ) ( A ( α jβ )) I Aj ( α jβ ) A ( j ) A j Re + + Re + I + = ; Re + + I + Re + =. (.3) ( -). " (.3) '!'/'! ( β #" #). (!.! (.3) ' β, #-'.

32 !!!* ( P 3 * U. (.3) )!' (!* "(, (.% /1' #. S r ' " 1.4. ).! ) #"(', ' # )..).$ )!" #-' /!* (...!*. (.! ). )!:!* $$. "!*!"!, ( #".( #.. # )!. )*.% #!!!"%!*.! %!, ((, '* # "! * U. )!' # )! $!'!(' * U.% #!!!"%. ", ( "- ( # #) (*! "..(. #.!*. (.!. ; #) )!' ' #!!!"% %!*/ )!*.!" #. (!*.

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36 s r ). 36 GU ). #) '*'!)!**!( s Θ j (.3). ##1'!( #!* (! #, - "!/(*, ( ).( "! "('.! ) #)!.*' )!)!*. s Θ Θ Θ Θ1 Θ1 Θ Θ1 Θ1 Θ.3!- ) * ). RS ". "! * * U S r,.) s RS s RS j. *' * U.! " T k " %' sr * = U )! * U ) " S r,

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38 .( #!(!)!/(* #. G j. 38 #",!. #.!" )!' )!' #. (!* )!!)/1 : 1. ) (.! ) (.16).. )! ) P, /1.( "('!*. 3. (.1) ) " P )!'!'!*,.( #. *'. 4. -) (1.1).(. "!!!"%. * U #! 5.,(' #' "%' P.! ) # ".(.. "! ( "!* #-.(. #. /!*. 7. +!"!-' #!!!"%!*.! )! #. (. &, (!* )' $$. (. '!* */!, 1.!( (! #) * ): ( ) * ( ) ( ) P( s) = B s + T A s, (.7) = k 1 j * j.) B( s) = ( bjs ), A ( s) = ( a, js ), T T T j= j= < <.

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41 ))1 "'' )!!* ). $$% ( (), ('.).!!(' + 1 )!,!-, " )! '' - '). "!* #!% #"' 41 /!- )!. P, ) ) ) #!% "/' ) ). # P, - "!/(*, ( )' #!% ") " # " #, '"/1 P. ( #!%.1 ) 1 )!'!*. (.! *. '), $$%. '!'/'!*. #!%.1 1 )!' (.! $$ )!*/ *. ') (!*!* $$%, )%) ) 1 T T 3 T T 1 T 4 T T 3 T T 1 T 4 3 T T 3 T T 1 T 4 4 T T 3 T T 1 T 4 5 T T 3 T T 1 T 4 6 T T 3 T T 1 T 4 7 T T 3 T T 1 T 4 8 T T T 3 T 1 T 4 9 T T 3 T T 1 T 4 1 T T 3 T T T 1 4

42 4 #",!. )!'.% #!!!"%!!* )!!)/1 : 1. ) (.! ) (.7).. )! )! (.!. 3. C!)!* )! (.! ') "' (#'). 4. C!* "('!, " ') "' (#')!. 5. C #.!)!* ".( "(! '), " #- #. /!*. 7. +!"!-' #!!!"%!*.! )! #. (. &!'!" $$ "#!. #! ) ' ( #-' #!* (! "!(!(!/ -) # "!(!(!* $$%. "!* ) )! #!%..3.

43 43 #!%.!*!" $$!. -)'!*. #.!* )! / #!*!!* )!*/ ', -) )-!(!( #' $-!* ( t # /t n!* ( $$% # (t # ) t # /t n (t n ) 4 5,55,,75 4 1,75,71, ,7 1,45,5517, ,3,83, ,3,35 3, ,6 1,3 3, ,8 3,1 3,4838 3, ,4 5,9 3, ,6, ,6 5, ,3 4,7 5,885 5, ,9 8,9 6,56 3* (.% #-'!*. (.! $$ )!*/ (#'!* # ) )!.7.

44 44.7 ' (.% #-'!* )!*/ (#'!* ) " ).!" $$ "#.. ) MATLAB!. (.% (.!!* )!*/ ), ( * (.% #-' ".(.!(!(!* $$%, / #. ( -)'!*. #. 6!* $$% ")'' # ( # ( # ) 6 ".!( ( "#' # (.%!(' %!* ' $$%, "'1!(!* $$% # ).

45 45 #!%.3!*!" $$!. -)'!*. #. $$ )! / #!*! $$ )!*/ ',!( )-!(- -)!* #' $ ( t # /t n $- -( #!* $% (t # ) t # /t n (t n ) 4 5,8,18 4,4444 4,, , 1,3 4 4, , ,7, 8,5 5 5,5,6 9, ,7 1,6 7,9375 8, ,8 3, ,8,5 15, 6 14,8,9 16, ,5, 15, , ,9 4,1 16,3171 3* (.% #-'!*. (.! $$ )!*/ (#'!* # ) )!.8.

46 46.8 ' (.% #-'! $$ )!*/ (#'!* ) " ).!" $$ "#.. ) MATLAB!. (.% (.! $$ )!*/ ), ( * (.% #-' ".(.!(!(!* $$%, / #. ( -)'!*. #. 6!* $$% ")'' # ( # ( # ) #!"!* 16 ".!( ( "#' # (.%!(' %!* ' $$%, "'1!(!* $$% # )..3. " [7], (!* )!!#!** * ( (.!' )!'' (...!*. (.!. )!(

47 !(!* $$%!( ".(., ( )! ")!*!# )!. %) )!'!" "! (!*. ).! "#' ) )!'!*, ).( #..( "! 47 )!* # (!*. 3 '.! ) # " " $$% $! * a.) a..! Θ!( n g= 1, a )' Θ = 18 Θ + Θ (.8) n g= 1 g Θ = Θ + Θ, (.9) Θ g Θ.! -) 1 */,! " U g-!/!' $% (.13), /1 ) ) (; j ). [111] (.8) (.9)!(!)/1! #-' g P.% #!: U #) )!-*.% #!!!"% ',! "% -)!*!*.! Θ * 18.). 3, (,.! (.8) (.9),.! Θ * #1'!'/1' n Θ, '!'!!'.(.!-' U. g= 1 g ) '.! (!( a $! Θ /.! Φ, Φ = π + Θ (.3),

48 48 * a $! Φ = Θ (.31) ) )( E )'1 " (! ) ).! Φ.! ")* "( Θ,,.! (.3) (.31),.! -). $$%!. )!'' #" (!' /1..!. (), ( "!-/ E - )* "! U. #) )!-*.% #!,! E!* $$% #)!.*'.!, * 18.). #!.!') *!.!' -.( #, ' E. )...9 (*'!* $$% " "-!- E )!'!('.(. 3, ( " )! $$%!*.!*! # "!' (* /1 18.). ; ) "-*, # ) ",!-*!* -! #".!)!*, # -!. $* )! $$%.( P.!" "-.!-' E - )!*!)/1 -):! )!' -). " $$% *. ). (.3) (.31) )!-,!/#!)!*!- #)!-*.!, * π,,!)!*, )!'* ).( P (.1).

49 49 #", ")'! 1' #' ( (!*. -) ", -!(* # " "-.( P.! $ # $ " " $! #.9 &.!-'.1.(.4. &!' )!'!. # (!!) (*!.% #!!!"% : # RS. )*.% #!!*/, ((, '* )! (. (!).!(', (

50 #., #" $$% a 5!(, )'1 " (! ) ).! a j, /' π ϕ = π. j U,.( ), ) (" #!(. *' )..!)!*, #) ( ). $ $ #.( P. &!'. )!.' )!* #!(,!-1 ").! γ..! π #!(, #! ", )'' $! ϕ = π, n k k =,1,,..., n.!-' #!( ".11.!.! γ "). )-' #!(, $.(!) )* #!/# Θ " )" π π < Θ < π. (.3) n! - γ )- #!(, #)!'* "/ %) Θ " (.3) " )!!*)" π π π < Θ < π, k =,1,,..., kax, n k + 1 n k + ax (.33) π π γ < Θ < π. (.34) n k + 1

51 51.11!-' #!(! -.( P '!'' #D) -,!( "!( "(' Θ.!(.( P )!'' $! k ( n ). = ' & 3 ## # % -('# &(' ( ('., #'+#4 #,##('. ).!" "#!)/1' %) $' #.( P. 1. &!' ").! γ (!!* $$% )!*.! #!(,!-1 AOD.. 3)* "(.! Θ " )" (.3). 3.. ). )!'!* $$% # )! *!(, )'1 " (! ) ).! (.33) (.34). 4.. )., ('!/#.!(, )!*!)!**!(,!- ) " ). )-!-!*! ( (!).

52 5. " /1!( )! $$% 5 $* ).( P. 6.!)!* "'' (!*!(, * %).4,5!(* ).( P. π 7.! π > π γ, * ) '. 3,4,5,6 "('.! Θ n " )" (.33) (.34). 8. -)!)/1 Θ #) "!(/1' #.( #* )#!'* )..5..,# ) # # -# 3'. 1. * ")!!* )!*/ [ 6;8] [ 14;18] [ 9,5;1,5] 3 s s s #) )!*!* # (...!*. (.!. )!.( # )!' P 3, )- 1 #. #- ) ". V 1 ) a = 6, a 1 = 14, a = 9,5 '!'' "! U1 = (,45 + j1,61)..! ) " U 1 #!* $$% /!)/1 "(': U1 Θ a = 54, U1 Θ a1 = 17, U1 Θ a = 31. )!'!''! (.6), # )./ V,!(/1/' ) a = 1,5. / "! U = (,31+ j1,5).! U Θ a = 57, Θ =, U a1 11 Θ =.!(! (.6) U a 141!'', * U '!''.( "!.!* (.3)!'' )!' ) )!* $$%, #- P 3 #

53 "!..( # " V )!'' " $$% $" U U Θ a1< a 53 Θ < Θ U a.!(. " 6 # ).1,.)! "!!*. $$% "(.!(,! " *. #% & "% ) "& % # &.1!*. #.. *!!* )!*/ D( s) a s a s a s a a [ 1; ]. = + + +,.) a [ ], a [ ], [ ] ,7;,1,3;,45 a1 1,1;1,5, #) )!*!* #!*. )!( P 4 #" (*'!* $$% )- 3 #. "!* # V ) a 3 =,7, a =,45, a 1 = 1,1, a = 1!, ( '!''.(.! ) # " #" U U U U U (,7; j1,4) / "(': Θ 3 = 89, Θ = 13, Θ 1 = 154, Θ = 17. a )!'/ #) )!' )!* "% P 4 $" U U U U Θ a < Θ a3 < Θ a< Θ a1. &!' ").!! (.3)!'' )!' ) $$% a 3 a. (.!( a a a

54 $".13.( # 54, )-1!* 1 #.. P 4..13!*. #. &!' "#.!. # "%,!( 1, # #! #- /!*. - ' P 3 P 4. #! #- (.. $$%. "!* #" #!*/!.% #!!!"% /1!*!, ( )!* ## )!-.!...,# ) -('# &('. 3. * ")!!* )!*/ D( s) a s a s a s a = + + +,.) a [ ], a [ ], [ ] ,7;,9,45;,49 a1 1,1;1,5, a [,1;,7 ]. #) %*. #/ (*.! γ = 7. #!%.4 ).( P 4,!( '. ).,.! "# ). '"/1 # #-

55 // /!!* ).% #!!!"%!-'- (..14). ) ".14, ' #!*!. '!*. (.!!-.! γ 4 = 6.!)!*, 55 ")!* (! #!) # (*/.! γ = 7. #!%.4 1 P 4 ) 1 a a a 1 a 3 3 a a a 1 a a 1 a a 3 a a a 1 a a 1 a a 3 a a 3 6 a a 1 a a 3 7 a 8 a a 1 a a 3 a a 1 a 3

56 56.14 #!*!!"%!*. (.! 4. ( #!"%.!, '1/ "..!,!), )(.!'! '-'. (! ) a s + a s + a s + a =, ) a3 = lj, a = J χ + χr (1 + Tk k ), 1 a = Jc + cr + k k r χ + Tc, 1 1 ( ) a = ck1k r,.", l )!..!, J %!), χ )!* $$% )$'..!, c )!*' -*..!, r ) ).!), k1, k $$%!'!( ( ) $$% )( -.!', T '' -.!'.

57 "(': 57 ' ##1. #D!' / J =.5', 4 χ = 1 1, c 4 = 1, r.1 =..!* ") )": [ 5,5] ', l [ 5,1], [ ] k1 5,5..!' k = 1, T =,1 )! )!' ) "(!*. #) "# %)!" #.!* ( *.(!*.).$ )!' ) #!"%! '-' )!* )!* "(' "! (. ) (! ) (.7): 1 l A1 ( s) + A ( s) + k1 A3 ( s) + A4 ( s) =,.) A ( s) = ck r + ( ck Tr + χk r ) s + χtk r s, 3 A ( s) 1 = Js 3 ; ( ) ( χ ) A s c χs r s ( ) = ( + ). 4 A s = J c + s s ; (.. #" '!* )- 8 : V (5;5;5), V (5;5;5), V (5;5;5), 1 3 V (5;5;5), V (5;1;5), V (5;1;5), V (5;1;5), V (5;1;5),.) ' ) ' l, *' k 1. &!' $% ) (.19) (... )! '!/ (3,34+j3,88, 3,34 j3,88, 1,53), - #! (! ' A ( s ) ; A ( s ) : 1 ; A ( ) 3 s : 1).&!'. "! 3,34+j3,88 (.4), (.5) ) Θ = 34, V1 V1 Θ l = 5, Θ 1 = 86..! )! (.6)!'',!)!*, V 1 )!- #., V1 V1 V1 l k1 V1 k Θ < Θ < Θ,,!)' "# ), "!)!** "'!* " V 1 (...: l k1 l k1 l. " ().( #!)/1 :

58 V1 V5 V6 V7 V4 V3 V1. #- //!!* )!,.)!* 1 #.(.!*...).$ #!*!!"%!*. (.!!!"%!* - %*.!*/ (*:!*' * (,35,!*'!#!** 3,8.). 5. * (! $$ )!*/ ): D s = s + s a + a + a + a + + a + a + a +, 4 ( ) 1 ( ) ) a 1 = [ ;5], a = [ ;5], a 3 = [ ;5], 4 [ ;5] a =. #) )!*!* #, *.).$.! ) (!*

59 % ( (!*/!#!**!*/ * (). a 1:, 59 )! )!.!: a :,5, a 3:,5, a 4 : ;!)!*, '* )!!* $$% #)!)/1!)!*: a 4, a, a 1, a 3, (' ) ".( ( (!#!* "('!* $$%,!#!*). "!* ") (!( #, )! !* #...).$ )!!* :!*'!#!** 1,15.),!*' * (,1.

60 6.6. ).! )!!' )!- #!*. (.!.( #!* $$ )!'. $" ', )!!' )!'.(.. "! )!' )!. "# ) )!'.(. #. )!'!*. (.! $$ )!*/ ( #!(. ", (!!* )'.!!* */, 1, "- 1 #!(!!!. )!' -)'.(. #. )( "* )! " ') "' (#')!)!* ".%!*, ('!* "(, )!*. "# ) )!'.( "! )!'!* )!*/. ", ( )!' -)' "! #) "- #!( )!* #.( )!' -)., #".!(. #.( #)! # ). ) ') (!,.!')!!//1 ##* "# )!" #. (!*.

61 61! 3. ' (& 4 ( #'% )' #'+#. ( (' '' (&,# ) 3.1.!- - ' (.!' (+) #D (* ( #D!' %!% "'/'! " " ". )!' "!* + " ), "# )!' #D ', '" #!* )'. /, )!' %!!( #" ))!* ". )..).$. &!'!('!* + ) %. "!' ( (!* */ ( η!*!#!**/ µ ) #), (# (.!!* +!.!*!!* ', '1 ' η,.! ϕ, ϕ = arctg( µ ). 3)( "!* (.!'!!"%!/!* + #!,!/# "- "('!* #D!'. + -.!', )!/ : 3.1 (.!' * +!* )!*/:

62 .!': 6 *!.!' )(/ $%/ - P ( ),.) K * -.!', )(' $%' #D!' ):.) A( s) = ( as ), = W n B( s) = b s, W s = K (.35) ( A( s) s =, (.36) B( s) ( ) b b b. j j j j j j= #) )!* -.!', #(/1!- #!!*. (.! ") (!/# "('!* #D!'. #!* "- "(!*-)! #-'!/!* ) #!!!"%!-'- " 1,.)!!"/' 1 ( 3.). 3. #- (... P n

63 63!* (! - #* " ): f ( s) = B( s) + KA( s) = (.37) $$%! (.37), ) " ) *, #"/ '.!*.!!!) /1 n P, 1 n # n. #) "#*!. )!'! K,! (.37)!./' #!,.!) (*, (,.! [94],!*'!#!**!*/ * (!* + )!''.. P. &!' '! ")( )!./'!)/1 : 1. )!* "-.( P, #-/1'.% #!,.. &!' -) ) )!* "(' *. K, /1' *..).$.%,. 3. &!' -).( )!*! ),..).$ #) )*' #!,. 4. &!'.( )!* (' )! ),! (.37)!./' ") #!,. &!'!"%.!*"' $" '..).$ [94] )!.! )..).$ " $$% )!' '. ).. " [11], ( )!'.( "% -)!*!*.! )!- * 18. [11] -!, (,.( ) #!!,. *' ). #!. ; #! ")!'/' #!(, )'1

64 " (! ) ).!: 64 π l ϕ =,.) l =,1,,..., z = 1,,3,..., n. " z!(!) #*,!-,.(..!!*!#!*. &!!) #* "!*.! -)!(,.! [11], )!' a a * / )..! Θ!-. 3 #) #* #%,!-1.! 18, #", )!* ).(. &!'!"%. '! ")(!*"' "..).$ )(- ; (,;) [11]:.) E( δ, ω ) = Re( B( s)), F( δ, ω ) = I( B( s)), P( δ, ω ) = Re( A( s)), R( δ, ω ) = I( A( s)), F( δ, ω) P( δ, ω) E( δ, ω) R( δ, ω) =, (.38) δ ω 1 ( ', )!-1.,;. )!'' (.38) '.%,, )!'/' "(' ω, ) ( #.%,. &!' )!*. -)' "( ) #)!*"*' -: K = E( δ, ω) P( δ, ω) + F( δ, ω) R( δ, ω). P ( δ, ω) + R ( δ, ω) (.39) )!'' (3.5)!( )!* "(' ω,!( "(' ), ) ( #.% #!,. * ) "( ) " )! )!'! ),! (.37)!-,.

65 65 ( ) (' )! ), )!'/1 -) " "-.(. ' & ( #'% -)': )!) "# )!*-(. " -.!',!/(/1'!)/1 : 1. 3) # "! ( (!* ) (!* )!#!*!* ).. -) "-.. P, #-/1'.% #!. 3. )! )!' -) ).( -' (.39), ( (' ") #!, */..).$. 4. )! ) ) "( " )! (.37)! "( *. K,..).$ )'' ") #!. 5. -) (' ).3! K )!.! K,!!./' ") #! )!'.(. &!' (. ' "# ) )!-.!. #! "#!-. MATLAB, )/1 1 $$ )!' "!* + ; !-!- (.!', )!/ 3.3.

66 66.!': 3.3 (.!' *!.!' )(/ $%/ - W.) K, K.!', * + P K s + K = (.4) s * + ( s), )(' $%' #D!' ):.) A( s) = ( as ), = W ( n B( s) = b s, A( s) s =, (.41) B( s) ( ) b b b. j j j j j j=.)!* (! - #* " ): ( K K s) A( s) s B( s). + + = (.4) + * #) )!* -.!', #(/1!- #!!*. (.! "), ( 3.)!/# "('!* #D!'. )!*! (.4) ) k c s =, (.43) =.) $$% c k. '!'*' $%'!* #D!'.!'.!* $$% c #"/ (..,. )!'/' "('.

67 67 "..).$ ", (! *!- 1,.! )..).$ ". '!'/! 18. (), ( )!'., (# 1 *!*.! ).!'! "!/#!* $$%, #), (#.! ) $$%!'! 18. #!* $$%, #( ) #, )!''!)/1. -)': '1# 1.!!* $$%! ") ()/1' )! cc1 cc3, ('!*. )!' c, ) # $$% )!' 1!/,.! ).).$ ".!* $$%!'/ 18. "&%'+('. " $"..).$ ", (.! ) " '!( $!:.) n Θ = 18 Θ + Θ, g= 1 g c - (.44) Θ g Θ.! -) 1 */,! " ' g-!/!' $%. *! (.44) 1 * S*..) )!'!/#!-'- )!'!/#. 1. ',!-1! S*,..).$ - "!/(*,( Θ 1 + Θ = 36, Θ 3 = ( 3.4). P P P

68 68 3.4!-'!)!*,.! ) " ' S*!( $!: *, c - Θ = 18 + Θ (.45) Θ = Θ (.46) #",!!*! #) * ()/1' )! $$% cc1 cc3,.! ) " #" /1 # (... P #) 18. ). -)' - )!* ), (!*' * (!* - #* ")!* ', )'1 (" 1 *, /1 ()/1' )! $$%!*.!. *!*' * ( ")' s* = α *. ) $%/ #! (.43), ")' ()/1' "(' b "( s* = α *. " )! K + (" K *,.!( -: v ( α ) K = f K, *, b, (.47) + * j

69 69.) v b j.( "(' $$%! B(s), #(/1 () )! c. &!' )!*. " -.!'!(!* (! ) * $$% v ( + ( * j ) * ) K K, α *, b + K s A( s) + s B( s) =. (.48) " [116], (,!(!* )! (.!,!*' * (!*'!#!** )!'/' #"..!* $$%, )!' '! ")( #) )!*. &!'. )!.'!*"*' ), "# [18].! -)' # ( #)..).$ )(-; [113] )!* )!' -) " "('..!' K *, ) (..).$ ") 3.3.% #!!!"%. )! )/ %), -!(* /1! "( K *,!*.!!- ") #!,. &!' -)'! "( K *, )!'/1.,!) (!. &!' (!*. )!' -.!' #) #* "( K * "!(.! )* "( - (.47))!' -)' "(' K +. )!) "# )!*-(. " -.!',!/(/1'!)/1 :

70 7 1. 3) # "! ( (!* ) (!* )!#!*!* ).. 3) (! s = α * )!!* #D!', /1 ) cc1 cc3. 3.!( " (.47) ) (.! )' * -.!'! ) * K *. 4. -) "-.. P, #-/1'.% #!,. 5. )! )!' -) ).( -' (.39) ( (' ") #!, */..).$. 6. )! ) ) "( " )! (.4)! "( *. K,..).$ )'' ") #!. 7. )! (' )! K *,!!./' ") #!, )!'.(. 8. # "(' K * " #! ('! )! "(' K + -' (.47). &!' (. ' "# ) )!-.!. - #! "#!-. MATLAB )!' "!* + ; -.

71 !-!"-, #$ % (.!', )!/ 3.5..!': 3.5 (.!' *!.!' )(/ $%/ &-.) K*, K+, K,.!', W P K* s + K+ + K, s ( s) =, (.49) s )(' $%' #D!' ): W ( A( s) ( s) =, (.5) B( s).) A( s) = a s, = n B( s) = b s, b b b. j j j j j j=.)!* (! - #* " ): ( + *, ) K + K s + K s A ( s ) + s B ( s ) =. (.51) &!' )- )( ). % "('!* $$% #D!' #) &-.!', # #(!!- #!!)/1 #": 1 )!-!.*' -) F 1 F,!* )!-!.*' #! ABCD,.(!* ',

72 7 )'1 (" F 3.! G, "/1!*/!#!** ( 3.6). #" #(' )!- 1, ) % #) )(!/# "('!* #D!' ") )!, "('!#!* #) *!* "). "(' !' #!*!-' ". )(*/ ). % )!*! (.51) ) k c s =, (.5) =.) $$% c k. '!'*' $%'!* #D!'.!'.!* $$% c #"/ (..,. )!'/' "('. &!'!!"% 1. ' ")! )! -)/ 1 )"!)/1 -):

73 73 '1#.!!* $$%! ") ()/1' )! 1 3, ('!*. )!' c, ) # $$% )!' 1 *,.! ).).$ ".!* $$%!'/. "&%'+('. " $"..).$ ", (.! ) " '!( $!:.) n g= 1, c - Θ = 18 Θ + Θ (.53) Θ g Θ.! -) 1 */,! " ' g-!/!' $%. *! (3.8)! 1 * s**..) )!'!/#!-'- )!'!/#. 1. ',!-1 s**,..).$ - "!/(*,( Θ 1 + Θ = 36, Θ 3 = ( 3.7). P P P g 3.7!-'!)!*,.! ) " ' s**!( c - $!: Θ = 18 + Θ (.54),

74 74 * Θ = Θ (.55) #",!!*! #) * ()/1' )! $$% 1 3,.! ) " #" /1 # (... P #). ). -)' - )!* ), (!*' * (!* - #* ")!* ', )'1 (" 1 *, /1 ()/1' )! $$%!*.!..! -)' 1, ) $%/ '!* */ (, ")/ s* = α1!* */ (, ")/ s** = α! (.5). *!*' * ( ")' s* = α1,!*' s** = α. ) $%/ # '! (.5), ")' ()/1' "(' s* = α1 s** α. =,!( : ( * +, α 1 3 ) ( * +, α 1 3 ) f K, K, K, *, c, c, c, c, = ; f K, K, K, **,,,,, =. c "(' (.56) (.56)!* K +, ' # ',!(: ( *, α 1 3 ) = ( *, α 1 3 ) f K, K, *, c, c, c, c, f K, K, **,,,,,. (.57) " K * " (.57),!( *, ( α α ) K = f K, *, **,,,,,, c, c, c, c,. (.58)

75 !(: 75 ) - (.58) ) " (.56), +, ( α α ) K = f K, *, **,,,,,, c, c, c, c,. (.59) &!' )!*. " &-.!' )!( ' (.58) (.59) (.5)!(!* (! ) * $$% ( + (, α α ) * (, α α ), ) K K, *, **, c + K K, *, **, c s+k s A( s) + s B( s) =. (.6) (.6)!)!(*..).$ )(-;,. )!' -) " (,!( ) [18] ), )!* )!' -) " "('..!' K,, ) (..).$ ").% #!!!"%,. )! )/ %) )!' -) (, -!(* /1! "( K,,!*.!!- ") #!,.!) (*, ( ) 1 * #'"!* #) )*'! α 1 ) α. &!' -)'! "( K,, )!'/1.,!) (!. &!' (!*. )!' &-.!' #) #* "( K, "!(.! )* "( -' (.58) (.59) )!' )!*. -)' K * K +. )!) "# )!*-(. " &-.!',!/(/1'!)/1 : 1. 3) # "! ( ( α 1, α, α 3, G).

76 76. 3) (! s* = α1 )!!* #D!', /1 ) cc1 cc ) (! s** = α )!!* #D!', /1 ) !( (.56) ) (.! ' * &-.!'! ) * K,. 5. -) "-.. P, #-/1'.% #!,. 6. )! )!' -) ).( -' (.39) ( (' ") #!, */..).$. 7. )! ) ) "( " )! (.51)! "( *. K,..).$ )'' ") #!. 8. )! (' )! K,,!!./' ") #!, )!'.(. 9. # "(' K, " #! ('! )! "(' K * K + - (.58), (.59). &!' (. ' "# ) )!-.!. - #! "#!-. MATLAB.

77 % " (.!'. "!' ( #) (*!*!/ "!*,!. "!-! " ( ). %. &!' %!'' #! ) ') (, * "!/(!*!)/1: #' )(' $%' "!' *!-'-!/, $!'!/,!- (!* */ (!*!#!*. &! ' *, #% ) /!-/ *!-'-!/, "(/!!(.!' ). %., )!' )( $% "!* ) P( s) ( s a1 )( s a )( s a3 ) ( s b )( s b )( s b ) = =, 1 3.) a 1 =, a = 5 6 j, a3 = j!* */ (, 3,5 ) *!/!( *, "#-/ 3.8:

78 78 3.8,$".!' ). % &!' )!' #!!-'!/!*..! ). % (.!' )# *! '.!' ( 3.9), "/1 "('.!' * )!-'-!/. 3.9 '...!'

79 79 ) ( - )!* ), ( ) "!.!' (.!' " "('!/ #)!', #!-/1' (/ 1 ). )! (! ).! #) **'. #", )!' #(' "). ( ). % #) (* -!-! " (.!'. &!'. )!.'! " (.!' " ( " (.!',! #), "' #!* ) "(.!'. &!'!"% %) "#!)/1' ): 1. # *!-'- )/1!/ P 1, P.. C%' '!/ ( #!*!#!**/!* */ (. 3. C%'! (,!-1 - #!- (! ). 4., #% ) /!-/ *!-'-!/, "(/!!(.!' ). %. 5., ( "(' *!/ "! "(.!'. 6. "). "('.!'!) "*.% #!, " " +.!) *, ( "# - ) MatLab.!" - %)

80 8 #!, (!. 1 #'!* #* -/ #!*, )!' ")..!' ( ".!' ).!' *-'. /, 1 '/, 31., ', 1 /. * ") (! ): K + a p + a p + a p =, ) a 1 = [ 1,13], a = [ 15;8], 3 [,95;1,5 ] a =. #)! K, #!!!"% ").! )'' #! φ = 1 η =. *!, φ = 1,,!)' [15], #) *!* ) ).!" ). )! "-.( P : a1 aa 3, a1 aa 3, a1 aa 3, a1 aa 3, a1 aa 3, a1 aa 3. &!,!)' "#. 3.1 ), )! K = [ 8,43;35,9 ]. &!'!(. "!*!*" "/ #/ #!!!"%!*.! K = [ 8,43;35,9 ] ( 3.1). " ), ( #!!!" ") #!,.

81 81 3.1!"%'!* -.!'. - *+-'. ' /. * ") )(' $%' " )( # '"*/: W p ( p 1) K p T s + K = s a s + a s + a.) K, T.!', p p 1 K ' $$% )( #D!',,

82 a, a1, a!* #D!', a = [,7;,8], a 1 = [,3;,4], [ ;3] a =. 8 #) )!* -.!',./1 α * = 1 ϕ = 1. ) ( ) ): c s + c s + c s + c = (.61) 3 3 1,.) c3 = a, c = a1, c 1 = a + K K p T p, c = K K p. ) (.61) /1 cc1 cc3.( "(' $$% a,!( "*: T p 3 a s + a1 s + a s + K K = K K s p p, (.6) ): (.6), ( ) 3 aα * + a 3 1α * + aα * + KK p as + a1s + as + KK p s + KK p =. (.63) KK pα *! #" (.63),!(: 3 K a s + a1 s + a s ( a α * + a1 α * + a ) s + K p K s. α * = (.64) (.64) ' )(-; ) (.39). ) [11], )!'..!* $$%, ) #1! K p,!!./' #!,: =,4733;5,16. # "( p K p K " ).!: K = 5,16 -' (.6)!( "(.. T =,4458. p #!!!"%!*. (.! ) -.!' )! p

83 !"%'!* -.!' 3. - *+,-'. ' ' 4. * ") )(' $%' " )( # '"*/: W p K p s + T + Td s K 3 s a3 s + a s + a1 s + a =.) K, T, T &.!', p d K = 1 ' $$% )( #D!', a3, a, a1, a!* #D!', a 3 = [,;,13], a = [,3;,34], a 1 = [,1;, ], [ 1;4 ] a =. #) )!* &-.!',./1 )( ) % )/1 1, )'1'! α 1 = 4 ) α = 6!*,

84 ',!-1 #!,.(!* */ ( α 3 = 14!*!#!**/ ϕ = 3. ) ( ) ): 84 c s + c s + c s + c s + c = (.65) ,.) c4 = a3, c3 = a, c 1 = a 1 + T d, c 1 = a + K p, c = T. ) (.65) /1 cc1 c3c3.( "(' $$% a, s = α1 = 4,!( "*: T = 16, K 16 T. (.66) p d ) (.66) /1 1 3.( "(' $$% a, s = α = 6,!( "*: T = 5, K 36 T. (.67) p d ' ' (.66) (.67), " K p T d : K p = 5, T. (.68) d ) (.68) (.66), " T T d,!(: T = 39, T. (.69) )!( -' (.68) (.69) (.66),!(!* (!, "!* T d, )/1 1 * - #).* ") " 4 ) 6: ( ) ( ) 4 T + 39, T + 5,797 + a s + d + T + a s + a s + a s + a s =. d d d (.7) (.7) ' )(-; ) (.39). "# ), )!' ))%..!* $$%, ) #1!!!./' #!,: [ 1,9;1,166 ] T =. d T d,

85 85 &!' (!*. )!' &-.!' '..).$ #.( (1,9; 1,166) ) ) (1,918) "(' " ).! T d. &! - (.58) (.59)!( "(' K p T. "!* ( ) #!% 3.1. #!% 3.1 ( $$% &-.!' B / T d K p T 1 1,9 15, ,391 1,918 16, , ,166 17,336 67,345 #!!!"%!*. (.! ) &-.!' )! 3.1, ,. 3.1!"%'!* &-.!'

86 !"%'!* &-.!' 3.14!"%'!* &-.!'

87 87 )! ) ( 3.15).$ ) % " )( ) ") -) ".( )!' T d = 1,9, K p = 15,9586, T = 64, ) %.( ). " - -)*, ( ) % " (.!' ' )( ),!/!* /'!- -! #!!/# "('!*.

88 88! 4. #) %* ) ' # % ( #'% #'+#. ( (' 4.1. MATLAB ( ), -,!)!', ) (.!' ( )'!'* (!, ")* ## "!*!*!), (* -,!'* (. 1/ %!", "!'/1!'* (! )! %. - ' (/' ")(,!)/1' )%,!# #/1!('!-!* )!,!# # '" "# #! $$ )!.!( #! $$ "'!*" #1 ( "!'/1 (!!#!( * )% ( ")(..),!)' ) #!*/ ' )(/ (/ )., - * *!) ")( '"(! ( ). #!* '1 '!(! #1( MathCad MatLab, "!'/1!'* (!,!( %. MathCad # ',. )%.., (!' ")'' ' - $! )' '/' $! %!* $, ( "!' * #( ). # ) ' -.(, ")' #!* (*/ (. &!' # MathCad!*"!' #/'!* "',.', (! ).

89 89 MatLab, )(.# ) '".', "!'/1 *. )% ), '' #( $!. # ##! ) ). $%, 1 1/. / "*!.. &!' $$ # MatLab, "'!..', (! ),!*"!* -!'* # ) '. '" " MatLab #!.), )!' '!..' "(' (! ), )!'!"%!) ")(..!. A #!* * $$ #" $%, -!( %!" ##! MatLab. "') #! )!'!)!* %!. MatLab (Matrx Laboratory) '!'' )!'!' - ( (, # ). MatLab "# $ MathWork Inc. (A+,.., (). )- / (/!/ $, ))-! %, % ), #!.#(!,! ")( "%,. ), )$$%!* ", "!( ).$,!.!( '".' )#' %' ) ". # ) ( $%, "!'/1' $!* #!!(* ', )# $ #.' )!"%. ). '".! ( "'..' "!'

90 9!"*!/#!. ) '". '.., )' )!/( %) $% '" C. 7" Matlab #( "-* # $! 1*/ )# $%..,!" ) )!.! )!'(' " $!. MatLab '!'' ( %) $% )!* )!'!*"', )!' % )$%. (,.',!*"!* ' "-., %) $%' ) ) $%'.!/(/ # %!" %$ ##.!,!" "! (.!',. )!' )(, ')!* " ". Maple V ).. &!'!" "!'!* Matlab 1!). Robust Control Toolbox, $!" ) "% H H 5 [6]. (', ( ), #! ", $$ )!'!" "!*, )!' "#. ) MATLAB %!".!)., #. *! ")(. " ) Robust Analyss and Syntheses of the Interval Systes (RASIS).

91 4.. & % '% RASIS 91!*! ): P( s) = a s + a s a, a a a, =, n, (.71) n n 1 n n 1.) n!*' *!*. (.!. MATLAB: 3)).% "'!* $$% a = a, a,..., a n n n n( n 1) n a = a, a,..., a ax ax n ax( n 1) ax,. (.7),% #) #"(* % -!#% (#"( < ), -! - #*!/! )% (!*!!* "(/, ). &!' -)'.(!*"'!)!*! # (# "(',! 1' '!''.( ).. #) n. #", (!.%: a, a,..., a, a n n n( n 1) n1 n.%: an n, an( n 1),..., an1, aax,, an n, an( n 1),..., aax1, a, n * an n, an( n 1),..., aax1, a ax. #",.% )( )!/ (#!% 4.1).

92 9 #!% 4.1 <.%. B,% '! #"(.% a, a,..., a, a n n n( n 1) n1 n a, a,..., a, a 1 n n n( n 1) n1 ax a, a,..., a, a n n n( n 1) ax1 n,,...,,,,...,,1,,...,1, a, a,..., a, a 3 n n n( n 1) ax1 ax,,...,1,1 a, a,..., a, a n ax n ax( n 1) ax1 ax 1,1,...,1, $ RASIS C%' defneallapexes (power) "1 %-, '1/ " )!'! ") power */!*. (.! ().!( "!*/1 %!(.!#% " 1,!!* $$%!* "(,!,!!*. C%' defnesectorapexes (power, beta) "1 %-, '1/ " "-.( )!'! ") power */!*. (.! () )!'!#!* beta. +!.(' $% ) 4.1.

93 5 $ A ( 5("#$%& $' (("$) $(* + +('-./!"#$%%& $' (("$) $(* (("+(,-./ /!( % +( '(( #B5$(( ( ( 5(C/$(('( 5(" +&+ $ $ ( 5('( $=> ;<=>CD $5 $ ( 5( %& ((% ( ) $''$( ';<=> &++ ()$( %+ (($C A! '( "((% (%# (5(%(% ( % '89:C?$5 ("$5 ( "((%& (%&# (5(%& (C $) % ( # (5(%( 5('( $(%& EFF(+$($' ("# (5("(%CG$ ( 5( (E ( 55-./+"+( $ ('( $(( 5( ( $(#EFF( CG$ ( 5( (H $(C +$( $(%"#$!(' % +) ' ( '+$ $(# ( 1( 3 4%$ $ ) $( ( ' # (5( '( ( "((" +$ $(, # (6 ( 7) ( "((, (, # (5(,( 89: /$$!( % ( ;<=>6 (?( 4.1 +!.(' $% defnesectorapexes

94 94!( "!*/1 %!( "-.(. C%' defneinterlacedapexes (power, frsteleent) "1 %- ()/1'! )%, (' FrstEleent. &! %- power. C%' defnetruncatedsectorapexes (power, beta, alpha) "1 %, '1/ " "-.( )!'! ") power */,!#!**/ beta */ ( alpha. C%' stintruncatedsector (Tn, Tax, apexes, beta, alpha) ',!, " apexes,!- (,.(!#!**/ beta */ ( alpha. "!* "1' 1,!!- ") #!!(. Tn Tax %-, "/'!*!* "('!* $$%, ('!*. :!- $% stintruncatedsector )! 4..

95 5 $ A % ( 5('( $(%& $(%&( 5(" ( $(%&EFF($' "+(-./ /$5( 5('( $ EFF(-./13 %+'%&( 13$) $( 13 +("5 13C!?(+$( %5$',' (("F("+ KLJMLN!! /$5+$( ( 5(' EFF( ((%& ( ( (( 5(" ((%& D%5$(+$( ( I $ (+$( J ((5(( # (5((#$ ( 5(6!(" ' "#$%& (?( 4. :!- $% stintruncatedsector

96 4.4. & RASIS 96 C%' defnemaxalphamnbeta (Tn, Tax, apexes) "1!*/!#!**!*/ * ( "('!* $$%, " Tn Tax.!*'!#!**!*' * ( )!'/', " apexes. ) %!*"' ' MATLAB $%' step. #/'!*!#!**/!* */ (. C%' edgetheorebuld (Tn, Tax, k, r) k-.$ #.. P r ( -) #. C%' fndcrosswthbandn (beta, alpha, T, TVar) ) ( ('..).$, "'/1.' *!'/1 TVar,.%, ") */ ( alpha!#!**/ beta. "' (* ")' T. &!'!"% ) $% '' )(- ;. C%' synthesbn (Tn, Tax, TVar, beta, alpha) )!*!* "(' $$% T k,.).$ ) ")/ #!*,.(/!*!#!**/ beta */ ( alpha. "- ' $%' "1 "( 1.

97 RASIS 1. *!!* )!*/ ) D( s) a s a s a s a = + + +,.) a [ ], a [ ], [ ] ,7;,9,45;,49 a1 1,1;1,5, a [,1;,7 ]. #) )!*, '!''! # (. "!*!' /1. RASIS!. )!' # ( (.!!* )!*/ #! )!, ( '!'' # (.. *!!* )!*/ ) D( s) a s a s a s a = + + +,.) a [ ], a [ ], a [ ], [ ] ;1 6;8 1 14;18 a 9,5;1,5. #) )!*!* #, #"*. /!* (!* % ( (!*/!#!**!*/ * (). # /1 ) ' RASIS ) (!* ). "!*!'.!( #-!!, )! 4.3 ()!'!* -)'!*. #. - " #- (.!!!) )!.. ').!!'. RASIS (!!!* "( (,,6557!* "(!#!*, 44,4345.).

98 #- (.!!* )!*/ )!' 4.1 *!!* )!*/ ) D( s) a s a s a s a = + + +,.) a [ ], a [ ], [ ] ,7;,1,3;,45 a1 1,1;1,5, a [ 1; ]. #) )!*!* #, *.).$.! ) (!* % ( (!*/!#!**!*/ * (). # /1 ) ' RASIS ) (!* ). "!*!'.!( #-!!, )! 4.4 ()!'!* -)'!*. #. -

99 " #- (.!!!) )!.. '): #- (.!!* )!*/!!'. RASIS (!!!* "( (,,4134!* "(!#!*, 7,834.).,( # " 1 #,.. 1 #!( #) '* # ).. ". ), ( 1 # "!,!.!)!** ) " "! ''. 3. 3) ) =, a s a s a K T

100 1.) a = [,1;,15 ], a 1 = [ 1;1,5 ], a = [ ],1;,, K T * $$%. #) )!*! K T, )'' (,.(.! ϕ = ± 45!* */ ( α =. 3 RASIS, # «)!!*! *. $$%, #(/1 / (*», ) #) ) ).! )' (!, )!)/1 : [,5;3,1 ] K =.!**!(. ',.(!*.).$.! # /1. RASIS,!( "!*, )! 4.5. T 4.5.(!*.).$! '.).$ )!)/1 (! "(':!*' * (:,5 : [,;1;1],!*'!#!**:,17 ) (1,.)) : [,1;1;41,4543]. " 4.5 ), (!./' -! #!!/#"('!* $$%.

101 11! 5. ((# &'+# ' "-1 ( (,+%# RASIS 5.1. "(-1!, #. ) -..! )"( )!'!(' )! $.,!*".. [8].,"" (,)!*.. &-1-13, ( 5.1) )"( )!' #. 1.!!#..!.( -)! )',!',!'%.'(. )#-'. )..!' ) 1 /( )!),3 º. 5.1!*.. &-1-13, %!*'!*... &-1-13, )! 5.,.) 1, - ##;

102 1 3, 4 '!* #..."); 5 (.'.); 6 $ ; 7, 8 #!! $. ; 9 ") ; 1, 11!! # "). (. ; 1! # ; 13, 14!! #!.#. ; 15 # #. (. ; 16 # ; 17.!; 18,.); 19 ).'; 1 ; #; 3!*'!'; 4 % ; 5 ); 6.!*; 7 )"!*!; 8 )!*!; 9 ; 3 ; 31 #) )( ).

103 13 5. %!*'!..!*.. &-1-13, ". 1 ()!.) -. ((.) ##, ) -) # ". '!* #!( 594., #"/ 3 4.")..,") ")! -) # (..) 5.")! ( $!).

104 14 )'' (* -. ## ' )-,!* (! /!*"'1, -,!/ )!'!. $ 118-/ #, #"/ : 6 )! $ ; 1! # ; 16 # (!.(!); 9 "). # )%. / - ) 51,5, ( ).'!(' ' %!'%'!. # % "!*% ## 1, - % ( -!!: $ 8,! # 13 (!.( ) ") ( 1.., $!! 8 ) ## (*' # 7,!- - #, -!!!. #. (. 13 (!.(,.) ) ## ) # 15,!- #. -!! 1 "). (. ) - ## # 11. ( $!! 8!- ).! 17. # '-!', ". (, $ ". (. ## " 1 "#-.!!. ##. ) "!* )!- * '.., ## )! )!.! (*! %),!''! 3, ( ) ), 1/.'! )/ ##.. ).' 19 )"( )!' -' *! (!.'! ((. )-.) )! (.) 18 (, )!' ) (

105 15."),..") 4 (.) (!). )(!* ) ")'! 3, #.!!'. ## 1!! % 4. # ")' ) 5. &!'!('..!*"/.!* 6,!/ #( " )! )' ') '!* #..")!. ##! : )"!* # 7, )!*! 8, 9, 3.! & ).")! " )!*!. #). '!*. ( #.") ")',!*" #)(.! ") )/'.! 17, #"' $!.'.! (.", " ( )%..!#, )' # ()% '.),.)! " (!)!!(.!# # )' ), %!/1. 3 (." 9 15 )' " (" (.) 18 )' ).' 19,.#/ (/.)! )'.") 3,.) )/! ( #.! 6 ( ).",.#' (./.) 5, )'.") 4 '!*. ( #! 5,!, )' "!!'/' )' ".!*' )! '.(' )% (" ) )'. ") ) #)!*! 3

106 16 )' ) #D. ## 1,.) '! ).! ' '* %!'%. 1- ( '!* #).!' ) ". ## 1 ' - ## '!* # 4. (,!-.") #! #! " (.". #"/1'' )'' * () )' ## '!* # 3,!-.") #! #! (.". - ( $ )!' ) ". ## 1 ( # 7 ))' $!! 8, )!'', #"/1'' # 6,!, )' ##. 3- ( ") )!' ) " -. ## # 11 ))' -!! 1, )!'', #"/1'' # 9,!-, )' ##. 4- (! # ( )!' ) ". ## 1 # 15 ()' #! -) ))' -!! 13!. #. ;!! 13 - ))' ) " -. ##, # 14,! (. ) )!''!!, #"/1'' # 1!. #.,!-, )' ##. 5- ( # 16) 1!''!.(!# (. ) )'' * () " %!'% )' ##,.) % 4 )!'', ) '! ) % %!'% ''.! %!(

107 17 1 ) #!/ ) 5!!''.!* 6 )!'!('... ' ) ")' ". ##!* () ).!'!. )(' ) ")' " ' (!: ( -!! -. ##. - ## ) )(!! ),!*"' )!'. ) )! '!.! #- )' )!*! 8 /1 : 9, 3, )"!*! 7. ")!! #)(, #, (.") " )!*!. ) - "'*' )", )! ))-/'!* " )! )!, ( #!!' #' "). - # #!. #!'!. ).!" % ") #D!' - $!*!)/1 ")( "%: #) #(* #!"%/ )!' ) "!.. " ( "' )!; #) #(* #!"%/ ' ) ##!.. " ) /1 ); #) #(*.! )! ") %!*/!. -.'!; #) #(*!.(!* )!, /1 ),, )!' #!'. ;

108 18 #) #(*!.(/.!"%/!*. )!' ## +,!*!* * ) ##. +('.!' ' )"( )!' ))-'!*. ' -) )!* )!."!. "!. '!- * ) ##! [8]. * ## "'' "-"!('! *' )!!' )!, "'!." )!' ##. ' " ) )! (!) - "!'.!' #!. "!, ( - '*' ( -)' #. - ' " - )! ( ) " ##) ) / %!'% ( -. #. ; #D''', ( )-.!' ' )D'!'/' #' [8]. #", " # (.!' '.( "1 -' ' ##!, ), '.!, ).. ; )! )!'/ #"* #!, " / %/. +('.!' ' ##.! )!- #(* )- ' ) )!: 1) " "1."!* )!' / )!- * ± ; ) (#" "1." 1%!* )!' / )!- * ±5 ; 3)!* % - #! (!!/(.!' )!- * [8].

109 19 * ##! "/!'. "1. " : " )!* ), "." #!', " )!, "!* ). "1 ) '!'' ' - «#» ',.. ". (!*, /1/ " "1/1. ") '. 7! «#'» - #D'*!)/1 #": " ),!(, )!! *', ) )!!* ),!( '. )!* * ( )* "-" ' )!* )..!' ' ) #(! #. )-' ' ) ##,!* (! "'!*,!*"! $ "('. '" #!! ")( (. " &-.!' "# ). / (/ )!* )!* (!' ) ##!.. - )* ), " 5.3,.)!!)/.( *!( '!, 1 T s + 1 " )(/ $%/ #), "!! ) '!, K T s + 1 " ), K T s " '! «#'» ' ) K T s + 1 )!' # )(/ $%/ )( ). &( ) (( '! «#'». ) #D!' '!'' * ) ##!..!* '!''! *.

110 11 K T s T s + 1 K T s K T s (' )!* (.!' ) ##!.. 3'!!.., - * (/ )!* (.!' ' ) ##!.. ( 5.4).,5 1s s ,4s 5 5s (' )!* (.!' ' ) ##!.. %' #D!' )( ") " 5.5.

111 %' #D!' )( ") 5..!"- "(-1 #" )( $% #D!' (##!.. #)),!( )(/ $%/ ): 89s + 1. s s s , ,4 : &, ( #D /!*, T '' ##!.. (-!(*' 1% "-" '!'. ##!..); K, T * «#'» '' «#'» (- "'*' %); T '' #) (-!(*' 5%).!)!*,!*' (.!' ) ##!.. ), " 5.6,.) a 3 = [ 157;3975,78], a = [ 791,8;11816,64 ], 1 [ 188,4;19,8] a =.

112 11 &H.!' )I 1 693,6 s a s + a s + a s *I ) 5.6 '!* (.!' ) ##!..!*"' RASIS )!' " &-.!' )!' ")!* +!)/1. : ) % )!- * )( );!*'!#!** )!-#* - 45 ;!*' * ()!-#* -,1. "!* " &-.!' #!!(!)/1 : K =,175, T =,1, T = 5,87; (.73) * +, K =,177, T =,1, T = 6,61; (.74) * +, K =,178, T =,1, T = 7,34. (.75) * +, 5.3. ) "(-1.(.).$,.! #, )!' +!( )!' " $$%.!' (.73) (.75) )! (5.7), (5.8), (5.9) (5.1).

113 (.).$ )!'.!' &-.!' (.73) 5.8.(.).$ )!'.!' &-.!' (.73)

114 (.).$ )!'.!' &-.!' (.75) 5.1.(.).$)!'.!' &-.!' (.75)!*'!#!** )!' -) "!*!' 45,!*' * (,1.

115 115 &!' "!( #!(.!' 5.11, 5.1 " %' )( ").( ( ) %.!' (.73)

116 ) %.!' (.75) "!* (. " &-.!'!* +!.. &-1!(, #!!!"%!*. (.!!- -! #!, ) % )( )!/#"('!*.

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119 Ackerann, J. Paraeter space desgn of robust control systes / J. Ackerann // IEEE Trans. On Auto. Control Vol. 5. N 6. P Ackerann, J. Robust control: systes wth uncertan physcal paraeters / J. Ackerann London: Sprnger-Verlag, 1993, 46 p. 3. An, S. Robust stablty of polynoals wth nonlnear dependent coeffcent perturbatons / S. An, W. Lu // Proceedngs of the 4th IEEE Conference on Decson and Control Orlando Florda USA, 1 P Arzeler, D. Robust D-stablzaton of a polytope of atrces / D. Arzeler, D. Henron, D. Peaucelle // Internatonal Journal of Control,, Vol. 75, N 1, P Barlett, A.C. Root locaton of an entre polytope of polynoals: t suffces to check the edges / A.C. Barlett, C.V. Hollot, H. Ln // Math. Contr., Sgnals. Syst., 1987, Vol. 1, B1. P Barsh, B.R. The robust root locus / B.R. Barsh, R. Tepo // Autoatca, 199. Vol. 6, B. P Barsh, B.R. A generalzaton of Khartonov s four polynoal concept for robust stablty probles wth lnearly dependent coeffcents perturbatons / B.R. Barsh // IEEE Trans. Autoat. Control Vol. 34. B, P Bhattacharyya, S.P. Robust control: the paraetrc approach / S.P. Bhattacharyya, H. Chapellat, L.H. Keel Prentce Hall, Chang Y. H. Robust gaa stablty of hghly perturbed systes / Y.H. Chang, G.L. Wse // IEEE Proc. Control Theory Appl. N, P Chu E.K. Pole assgnent for second-order systes / E.K. Chu // Mechancal systes and sgnal processng,, N 1, P

120 1 11. Foo, Y.K. Root clusterng of nterval polynoals n the left sector / Y.K. Foo, Y.C. Soh // Syst. Control Letters Vol. 13, P Henron, D. An LMI condton for robust stablty of polynoal atrx polytopes / D. Henron, D. Arzeler, D. Peaucelle, M. Sebek // IFAC Autoatca, 1, Vol. 37, P Henron, D. D-Stablty of Polynoal Matrces / D. Henron, O. Bacheler, M. Sebek // Internatonal Journal of Control, 1, Vol. 74, N. 8, P Henron, D. Ellpsodal approxaton of the stablty doan of a polynoal / D. Henron, D. Peaucelle, D. Arzeler, M. Sebek // IEEE Transactons on Autoatc Control, 3, Vol. 48, N 1, P Henron, D. Postve polynoals and robust stablzaton wth fxed-order controllers / D. Henron, M. Sebek, V. Kucera // IEEE Transactons on Autoatc Control, 3 Vol. 48, No. 7, P Henron, D. Robust pole placeent for second-order systes: An LMI approach / D. Henron, M. Sebek, V. Kucera // Kybernetka, 5, Vol. 41,N 1, P Kawaura, T. Robust stablty analyss of characterstc polynoals whose coeffcents are polynoals of nterval paraeters / T. Kawaura, M. Sha // Journal of Matheatcal Syste, Estaton and Control, B 4, P Keel, L.H. Robust stablty and perforance wth fxed-order controllers / L.H. Keel, S.P. Bhattacharyya // Autoatca 1999 N 35, P Keel, L.H. Robust, fragle or optal? / L.H. Keel, S.P. Bhattacharyya // IEEE transactons on autoatc control, Vol. 4, N. 8, 1997, P Maar, N. Pole placeent n a unon of regons wth prespecfed subregon allocaton / N. Maar, O. Bacheler, D. Mehd // Matheatcs and Coputers n Sulaton, 6, N 7 P

121 11 1. Markus, A. H. The Khartonov theore and ts applcatons n sybolc atheatcal coputaton / A.H. Markus, E. Kaltofen // Journal sybolc coputaton, 1997 P Melnkov, U.S. Stablzaton of undersea object stuaton, connected wth shp by the rope / U.S. Melnkov, S.A. Gavoronsky, S.V. Novokshonov // KORUS 99 III Russan-Korean nternatonal Syposu. Novosbrsk, Russa, P Nesenchuk, A.A. Root locus felds technue n the uncertan control systes synthess / A.A. Nesenchuk // Proceedngs of the 5th World Multconference on Systes, Cybernetcs and Inforatcs. Orlando, FL, USA. 1. P Pare, T. Algorth for reduced order robust H control desgn / T. Pare, J. How. // Proceedngs of the 38-th conference on decson and control, Arzona, 1999 P Rao, P. Robust tunng of power syste stablzers usng QFT / P. Rao, I. Sen // IEEE transactons on control systes technology, 1999, Vol. 7, N. 4. P Rsky, G.V. Root locus ethods for robust control systes ualty and stablty nvestgatons / G.V. Rsky, A.A. Nesenchuk // Proceedngs IFAC 13th Trennal World Congress. San Francsco, USA, P Senel, W. Desgn and analyss of robust control systes n PARADISE / W. Senel, J. Ackerann, T. Bunte // Proc. IFAC Syposu on Robust Control Desgn, Budapest, Hungary, Senel, W. Robust control goes PARADISE. / W. Senel, J. Ackerann, D. Kaesbauer, T. Bünte // In Proc. EURACO Workshop on Control of Nonlnear Syste: Theory and Applcatons, Algarve, Portugal, P Soh, C.B. On the stablty propertes of polynoals wth perturbed coeffcents / C.B. Soh, C.S. Berger, K.P. Dabke // IEEE Trans. On Auto. Control Vol 3. B 1. P

122 1 3. Soh, Y.C. Generalzed edge theore / Y.C. Soh, Y.K. Foo // Systes & Control Letters, 1989, Vol. 1, N 3, P Soh, Y.C. A note on the edge theore / Y.C. Soh, Y.K. Foo // Systes & Control Letters 199, Vol. 15, N 1, P Soh, Y.C. Generalzaton of strong Khartonov theores to the left sector / Y.C. Soh, Y.K. Foo // IEEE Trans. On Autoatc Control, 199, Vol. 35. P Solyo, S. A synthess ethod for robust PID controllers for a class of uncertan systes / S. Solyo, A. Ingundarson // Asan Journal of Control, Vol. 4, N 4, P Soyleez, M.T. Fast calculaton of stablzng PID controllers / M.T. Soyleez, N. Munro, H. Bak // Autoatca 39, 3, P Taga, T. Desgn of robust pole assgnent based on Pareto-optal solutons / T. Taga, K. Ikeda // Asan Journal of Control, 3, Vol. 5, N, P Tan, N. Coputaton of stablzng PI and PID controllers usng the stablty boundary locus / N. Tan, I. Kaya, C. Yeroglu, P. Derek // Energy Converson and Manageent, 6, N 47 P The basc defntons: the stea boler. Retreved 7, fro the Web ste of the Boler Wkpeda, the free encyclopeda: Varga, A.A. nuercally relable approach to robust pole assgnent for descrptor systes / A.A. Varga // Future Generaton Coputer Systes, 3, N 19, P Vceno, A. Robustness of pole locaton n perturbed systes / A. Vceno // Autoatca, 1989, Vol. 5. N 3. P Wang L. Robust strong stablzablty of nterval plants: t suffces to check two vertces. / L. Wang // Syste and control letters, 1995, Vol. 6. P

123 Wang, L. Khartonov-lke theores for robust perforance of nterval systes / L. Wang // Journal of Matheatcal Analyss and Applcatons, 3,Vol. 79, N, P Wang, L. Robust stablty of a class of polynoal fales under nonlnearly correlated perturbatons / L. Wang // Systes and Control Letters, Vol. 3, N 1, 1997, P Wang, Y. PID and PID-lke controller desgn by pole assgnent wthn D- stable regons / Y. Wang, M. Schnkel, K.J. Hunt // Asan Journal of Control, Vol 4, N 4, P Wang, Y. The calculaton of stablty radus wth D stablty regon and nonlnear coeffcents / Y. Wang, K.J. Hunt // Proceedngs of 3rd IFAC Syposu on Robust Control Desgn, Czech Republc,, P Wang, Z. Deternatve vertces of nterval faly wth J-stablty / Z. Wang, L. Wang, W. Yu // Journal of Matheatcal Analyss and Applcatons Vol.66, N,, P Wang, Z. Iproved results on robust stablty of ultvarable nterval control systes / Z. Wang, L. Wang, W. Yu // Proceedngs of Aercan Control Conference, Denver, Colorado, USA, 1, P Xao, Y. Edge test for doan stablty of polytopes of two-densonal (- D) polynoals / Y. Xao // Proceedngs of the 39th IEEE Conference on Decson and Control,, P Zadeh, L.A. Lnear syste theory / L.A. Zadeh, C.A. Desoer McGraw- Hll, Zayatn, S.V. The robust sector stablty analyss of an nterval polynoal / S.V. Zayatn, S.A. Gayvoronsky // 1st Internatonal Syposu on Systes and Control n Aerospace and Astronautcs, Harbn, Chna, 5, P Zhabko, A.P. Necessary and suffcent condtons for the stablty of a lnear faly of polynoals. / A.P. Zhabko, V.L. Khartonov // Autoaton and Reote Control, 1994, Vol. 55, B1, P