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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

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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 * 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 1 3 1 3 ) K = f K, *, **,,,,,, c, c, c, c,. (.58)

!(: 75 ) - (.58) ) " (.56), +, ( α α 1 3 1 3 ) 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. 3) (! s* = α1 )!!* #D!', /1 ) cc1 cc3. 3. 3) (! s** = α )!!* #D!', /1 ) 1 3. 4.!( (.56) ) (.! ' * &-.!'! ) * K,. 5. -) "-.. P, #-/1'.% #!,. 6. )! )!' -) ).( -' (.39) ( (' ") #!, */..).$. 7. )! ) ) "( " )! (.51)! "( *. K,..).$ )'' ") #!. 8. )! (' )! K,,!!./' ") #!, )!'.(. 9. # "(' K, " #! ('! )! "(' K * K + - (.58), (.59). &!' (. ' "# ) )!-.!. - #! "#!-. MATLAB.

77 3.4. % " (.!'. "!' ( #) (*!*!/ "!*,!. "!-! " ( ). %. &!' %!'' #! ) ') (, * "!/(!*!)/1: #' )(' $%' "!' *!-'-!/, $!'!/,!- (!* */ (!*!#!*. &! ' *, #% ) /!-/ *!-'-!/, "(/!!(.!' ). %., )!' )( $% "!* ) P( s) ( s a1 )( s a )( s a3 ) ( s b )( s b )( s b ) = =, 1 3.) a 1 =, a = 5 6 j, a3 = 5 + 6 j!* */ (, 3,5 ) *!/!( *, "#-/ 3.8:

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

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

8 #!, (!. 1 #'!* #* -/ #!*, )!' ")..!' ( ".!' ).!'. 3.5. 1. - *-'. /, 1 '/, 31.,.3...1 31.', 1 /. * ") (! ): K + a p + a p + a p =, 3 1 3.) 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 3.1!"%'!* -.!'. - *+-'. ' 1.1 1 /. * ") )(' $%' " )( # '"*/: W p ( p 1) K p T s + K = s a s + a s + a.) K, T.!', p p 1 K ' $$% )( #D!',,

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 #!!!"%!*. (.! ) -.!' )! 3.11. p

83 3.11!"%'!* -.!' 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!*,

',!-1 #!,.(!* */ ( α 3 = 14!*!#!**/ ϕ = 3. ) ( ) ): 84 c s + c s + c s + c s + c = (.65) 4 3 4 3 1,.) c4 = a3, c3 = a, c 1 = a 1 + T d, c 1 = a + K p, c = T. ) (.65) /1 cc1 c3c3.( "(' $$% a, s = α1 = 4,!( "*: T = 16,579 + 4 K 16 T. (.66) p d ) (.66) /1 1 3.( "(' $$% a, s = α = 6,!( "*: T = 5,1115 + 6 K 36 T. (.67) p d ' ' (.66) (.67), " K p T d : K p = 5,797 + 1 T. (.68) d ) (.68) (.66), " T T d,!(: T = 39,4896 + 4 T. (.69) )!( -' (.68) (.69) (.66),!(!* (!, "!* T d, )/1 1 * - #).* ") " 4 ) 6: ( ) ( ) 4 T + 39,4896 + 1 T + 5,797 + a s + d + T + a s + a s + a s + a s =. d 3 4 5 1 3 4 d d (.7) (.7) ' )(-; ) (.39). "# ), )!' ))%..!* $$%, ) #1!!!./' #!,: [ 1,9;1,166 ] T =. d T d,

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 15,9586 64,391 1,918 16,6474 65,691 3 1,166 17,336 67,345 #!!!"%!*. (.! ) &-.!' )! 3.1, 3.13 3.14,. 3.1!"%'!* &-.!'

86 3.13!"%'!* &-.!' 3.14!"%'!* &-.!'

87 )! ) ( 3.15).$ ) % " )( ) ") -) ".( )!' T d = 1,9, K p = 15,9586, T = 64,391. 3.15 ) %.( ). " - -)*, ( ) % " (.!' ' )( ),!/!* /'!- -! #!!/# "('!*.

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

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

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).

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).

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,...,1,1 4.3. $ 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!( "!*/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

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 4.5. RASIS 1. *!!* )!*/ ) D( s) a s a s a s a = + + +,.) a [ ], a [ ], [ ] 3 3 1 3,7;,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 [ ], [ ] 3 3 1 3 1;1 6;8 1 14;18 a 9,5;1,5. #) )!*!* #, #"*. /!* (!* % ( (!*/!#!**!*/ * (). # /1 ) ' RASIS ) (!* ). "!*!'.!( #-!!, )! 4.3 ()!'!* -)'!*. #. - " #- (.!!!) )!.. ').!!'. RASIS (!!!* "( (,,6557!* "(!#!*, 44,4345.).

98 4.3 #- (.!!* )!*/ )!' 4.1 *!!* )!*/ ) D( s) a s a s a s a = + + +,.) a [ ], a [ ], [ ] 3 3 1 3,7;,1,3;,45 a1 1,1;1,5, a [ 1; ]. #) )!*!* #, *.).$.! ) (!* % ( (!*/!#!**!*/ * (). # /1 ) ' RASIS ) (!* ). "!*!'.!( #-!!, )! 4.4 ()!'!* -)'!*. #. -

" #- (.!!!) )!.. '): 99 4.4 #- (.!!* )!*/!!'. RASIS (!!!* "( (,,4134!* "(!#!*, 7,834.).,( # " 1 #,.. 1 #!( #) '* # ).. ". ), ( 1 # "!,!.!)!** ) " "! ''. 3. 3) ) + 1 + + =, a s a s a K T

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

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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 #) )( ).

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

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!' '!'' * ) ##!..!* '!''! *.

11 K T s + 1 1 T s + 1 K T s K T s + 1 5.3 (' )!* (.!' ) ##!.. 3'!!.., - * (/ )!* (.!' ' ) ##!.. ( 5.4).,5 1s + 1 1 s + 1 1 188,4s 5 5s + 1 5.4 (' )!* (.!' ' ) ##!.. %' #D!' )( ") " 5.5.

111 5.5 %' #D!' )( ") 5..!"- "(-1 #" )( $% #D!' (##!.. #)),!( )(/ $%/ ): 89s + 1. s s s 3 1884 + 9796,8 + 188,4 : &, ( #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 =.

11 &H.!' )I 1 693,6 s a s + a s + a s 3 3 1 *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 5.7.(.).$ )!'.!' &-.!' (.73) 5.8.(.).$ )!'.!' &-.!' (.73)

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