Réalisation et identification de systèmes bilinéaires homogènes Gibran Etcheverry To cite this version: Gibran Etcheverry. Réalisation et identification de systèmes bilinéaires homogènes. Automatique / Robotique. Université Paul Sabatier - Toulouse III, 2006. Français. tel-00130071 AL Id: tel-00130071 https://tel.archives-ouvertes.fr/tel-00130071 Submitted on 9 Feb 2007 AL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire AL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Laboratoire d Analyse et d Architecture des Systèmes du CNRS Ecole Doctorale Systèmes Spécialité : Systèmes Automatiques Par Gibran ETCEVERRY DOGER Réalisation et Identification de Systèmes Bilinéaires omogènes Directeur de Thèse : André MONIN
! " " # " " %&' " ( ) * " ) " ",) &, -
! "#% &'() " *, "# -.(),!/. "0%../ 0 1% 1'0 23 ) %! 4 ' &"# ) 10 % 3,! 1 ". " 1 0 "- % )1 & "" 0% ' 6 *1 "."6# " 4! 10% %,1# ( 1 7!/ # % 10 1!" 1 1 0 " 0 " " #8 9 1,: % # %!4 " % * / 1 " % ; 41 8 8 8
)')).).) ).6?)**)'.A)6*)*)-)A.) B! " # )A)))))C)! *. *)'*)))*)() )*)))*)()DE)A7)AD))7)) F % %&'( F '))))'.*)')(7) G B ').?)*)D))7))6&)) ) * # ) )& ), I '))))J)-*)&) K ),!!!""# *. FB )*)D)))) FI -,.& / *)'.*)D)))) B -,.& F )*)D))7))6&)) BF -, 01 B *)'.*)D))7))6&)) I -,.&& #! %"&' F )E)A))) IG F )E)A)?*?) IK % 11.,,2%34 '&!"''
( )* #6 L #6 -L F.1 " IG F ) # IM F A# IK F FA# G F BA# G F I0 #F F 1 J BN" "% F G0 #" " - 1 J BN" "% GF G (,-.,/ F 1 # GF
0(0 ( / / # "% O"MP ( / # 1 1 / 0O."KMP 1 /0 ( / # % 1Q / #O"KMP (,//%% "% 4 % / # /% 3 " ( ) R / #/% " /0"%. %% 0 ( 1 " O( &P 0? AS/ # O."P A " 1 /0 ( 1 / # 4 " 1%OL P., % (!" / / # - 0% 1 0 - ) % 4 " 0 0 / %% 0 ( 4"T1-4-1% /3 " ( ) & & & R 1 ( & "T)11 # /0 1 A0-
0 %1 "% 0 ) " # 11 " / ##%# 4 "# "/% 1 4 " 1 * ( 4"T1 /0, 11 %, / # "#. 1% # "%0 ( "! 1 "# 1 / #0 ( 14/0 # % # " " % / # 4 ) 11 # 4 "" / # J "% / # 2 J % * /0 ( 4 / # # 1 / # % # %3 "" / # %0%0 J -4-2! J " 1 / # 11 % 4! "%!%4!". " % / % "% " " 4 1 # / # "# J - 1 % 4. 11 4 # 1 " " " 1 / #/%/ # "# )1" F %% 1 / #% %%
,(.(.(),0( 1 2 03,. 1Q "!. " 4 0% 3UR- 1 VW U? # "VW 1 / #! # #BB 0# U 1 / #W O!BP % 1 1 / #1 A0 B / "% 1 0# 6 L.0- # U W #( / " 1 / # UW % /9 0 U" 4 W O)))BP A 9 KKB/ 1 / # " # " U2 W. " 4 / # 1, #0 4 # 1 / 1 4 % / %%1 " %"O KB!P KKB "% 1 "% 11 " 4. 1 / # KK4 1 / # 9 # 9 " 1 X" 1-9 O)))KP ) KMB 0 #% / - / # # E Y "E %4 //( 11 OMBMBP 11 KM 0 1 L ( % 1 / # 0 0#6!4 / 1, ""
1 / # 4 % A / # " 1!4 O7M!MP ' 1 &Z.0-/ 1 1 / # O&P ), 1 / # -4- " " 0 " 3 - " #" * 0 %", "1 1 / # " #, 11 " O(P F
B 3,.,0( 1 2.3, % / # 4 / #1 4 2 6.2 2 R 2 R. R 6 R, R, 4 R 2, R 4, 7*.- 13 4 R R R, % 4 % 2 8 3 6. 4 4 % 4 &.4 6Z ( ) ( )13 & & & & & & & & & " α α α 9 9 9 %"1 3 " Γ Ω
Γ. F. Ω 6.6. 6 B. 9 / # 9 11 % 1 * " 4/ # A 1 % 1 # 3 Γ 3 Γ 3. I R 3: Γ Γ 1,4 4: / ## 3. 6Z - # % # 1 / # -4-8;.1 6Z" Γ Ω % Γ Ω Γ % Ω 6 F. Γ 3. ( Γ 3 ) Γ3 G % % " 2, J / # % 1 6Z 1 # " 4 - # ) 11 # "1" 0%3 R % R #" R0 R 3 R " 11 1 Γ % J Ω % J 3 1 1 I
(),0!(-, ) % / # 11 % 1 4 A 11 " " % 4 # 34%/ # J ) 11 1 % & "% % " % 4 0 0 A1 / #!1 4 ) % 6Z! * " 11 " 04 " -4-4 4 - # 4 % # 4 4 " 1,60 J % 1 # A 1 6Z 3 9 9 α α 9 α 9 9 α α 9 α 2 2 9 R α / #1% % 3 Γ α Φ α M R G
4 6 4 Φα.6 6 4 K ( ) ( ) α. 6 6 4 A1 Φ α! ".! 13 - A1! " 3 Π ( ) ( - ) ( ) "! Π Π ) 0 " 0 M 3 Π Γ α Π # Π Γ α ) % α %/ # Γ α %#1 / # 1 "0 % 1 # 4 Π 3 Π 0 % 3 0 % 3 R UW 0# U W % "0 % 0 0 * 3 Γ α 0 F. % F I- G. Φ! % M 4" # F3 0 4 ( ) ( ) 0 Γ ( ) Φ ( ) 0 α 0 ( ) 0 0 ( ) Φ 0 0 3 M
% 1 4 " - 0 0 3 0 ( ) 0 Φ B R0 6 4 0 K / 0 "% 41% - 4 " 3 " %.( / OKP:("3 "! -) O("KFP: ((" * 3 " # " 1 / 1 O(K (KFP 11 " 0 3 %4-4 / # 3 * 0 % / # / #% *. 4 # / # A04/ #" %/ #/ " 4 " U W A) A ) " % "% ( ( ". 11 *0 / 11 3 0\0O(KBP % "(-F* 1 4 / 1 "1% \ "F* A) 1- O'P, -.3,*33,. /%% 0 1 / # 013 2.2 9 2 6? I 2 4 * K
R 9 9 9 9 R 9 R, 1 / # SZ 0 %% R R 1,,1 R 1 "%0/ # / # *? O'KKP! * 1Q " / #, 1 3, 7?, ( 1? 1 * 1 ) 0% δ,1 G *, % 1% 1 / # " 0 11 / # % X" 1 A "%4U% WO."P / # 4 1 # "% # "% A #. 9/ # I" 1Q % ' 6 4 # O(KKPO(P #, (0(2. ", 8. / # U W 1 #.- 0/ # % #6 % / # /% % # L ):; 4 1 4 ):; 1 9 * #6 L
* 1 % ):; / # /%4 A#6 % 3 %L 3 ( ) ( ) φ & φ M ψ & & ( ψ ) & K R / # & /%. # "" "% 1 A 0 "%)A4 1 # L 0 3 A A R 1 OL KIP % 1 / # # 6 L " / (* ( * O&P A " 1 # 6 " F* U" 4 W "O& "BP / L -6 1 /0( 4 "U WOSIP #/ 3 4 ):; *:; 1 R * #L -6 ψ & & ψ ( ψ ) ψ
& /0 ( 4, # 4 11 * ( " 3 ( ) " 11 "/0 3 ( ) ( ) & & & & & & & & & " R & & & 11 / ( 4 L / #& % 3 & " " R8 &
,.3, A 1 / #! - R E! R E.! 3 * 4 F * # %! 1 / 1 1 # 1 3! () 9 () B A 1 1 % /9 0% /% / # 0 # 1 / # O!KKP3 ( ) ( ) () 4 ( ). ( ) 6 I ) R / # %%.6) 4 /9 ; R 3. ( ) 6 ( ) )() () 4 ( ) R # 8 /96 1 1 # F * %,3 ( ) * 9 G
R % *^ ^ _; %%^^_; 0 3 3 ( ) * 9 M * *, * ; / *R # G- M3 9 ( ) 9 () * * 0 F^_;3 K () *! 4,,3 ()! * 0 K 3!! 1 403 ( ) () 9 () * () 9 ()! ()! () O 9 () P 9 * / # / / # Q 0 B3 6 ( ) ()! ` ( ) () 9.()) ().() 4( ) R I 1 4 3 4( ) 6 ( ) (). ( ) ( ) ) ) 1 3 F
R1 () () () () a 4 6.() ) a () () 6 ) (). a 4 () a () #, 1 3 θ ϕ θ R # A ϕ θ 03 θ ( ) F ϕ θ ( b b b b ) B R0 0."% / 411 1 ) B % "%/9 3 - /9. - /96 - /9) - a /9 a /94 - R%%.B. % " / # / " 4."0 B: 1 "" 4 /9 0 I % 11 0 %% # 3 )' /9.c)cc4c B
6C70Z/9.c.7.D E /9)c4c F E )/9.cc4c B.D E /9)cc4c % 10, )11 ϕ θ -, # AF # " % 4 # A/%% ϕ θ # # 4 A 1 3 a I %! 1 " 1 # / #% # 4 11 %"T10 13 3 ( θϕ ) b ( ) G A # 0# 3 3 ( θ ϕ ) ( ) θ θ / 1 4"%9 3 θ ϕ ϕ ϕ M % ϕ θ A a a % M 1Q #, 0.3, * - / # 3 - /E Y " E % #/011 I
- ( - # 0 - / # " - % 1 " / #!4 *# / /0 11% "/0( O6KKP 3,0(1 # E % - / # 1 1% 3 ( ) K R 1 / # # : % /9 3 R θ θ 2 a F θ F /9 3 # 8 8 ; G G G;J88 88 0# 3 θ ( θ θ θ ) F "% 1Q 3 2, 2 : : 1 θ,1, 1 : F R,818 J8%%2 F a b G
M / # F 3 θ ϕ θ FF R ( ) 2 2 θ θ ϕ FB 3 a FI 3 2 2 θ θ ψ θ θ FG % A " % # 0 # * 0 #%% 0 O."MKP " 1# %4 O."MKP 0 11 # *#" # 0/ 3 : : : : : : : : : : : : : : : : : : : : : :, 1, 1 1, 1 1 1,,, FM R, : 1 1 / # -! # % /01 / # 4 1 / % % % # 0 "OAZMP
3,03 (%0., ( 1 % 3 ( ) " FK R " 1 /0 ( 0 " OS"MBP "% " /0( & OSKP 1 ( 1 1 / # R " 4 & " "&-" O "KIP " 1 FM * " ( & / # % 1 /0 9 % *# 1 0 " O&KKP " &/96 1/0( # L # 1. " " 11 /0( OP ' 1" 1 UW #( 6 ", 0 3% % %2 * % * 0# % & /0 ( 11 1 SZOSBP 3,0,0(2..3,33,. # 1 ##E / " /0 ( 1 / # % 3 : : : : : : B K
R # 0 # 1 4 / #"/%:20/ # O "MP " 1 /0( / ## "OMFP A " 1 / # 4 # -. 0 0 " 1 O'MGP. " % 1 # O*MKP # # /! 0 / &. 11 1 # O "KP * " 1 / #17/ 1 4 # /" &. - / #! OKMP " UW 11 # " 1 " " % 1 1 O"KKP " / - / " % 1 * 1Q %OP. F 1 /0 (. / # 1 R / # 11 # 11 " % 1 0 &OP 1 UW/ # 4 / # % & 1 % / 0 OSP
!0.10,. / 0 / #%% 1 0 4 % 0 / % /% 0 " 1 O6KKP.0 ( 11 / / # % # /0/91 *" //( % 1%/0 * "/ "#, / # / # "# % ( 1 4 /0 1 % / # A - 1 1 / # - 4-# )11 -%# % %
!.Q 0 - / # 1 4 3 " ( ) R / # " ( ) / 1 / # % 1 4 %/ # / # 14 U1W -,0/1 3??? ( )? ( ) / # 1 4 1,, 0 1 (.- / 1 3 " ( ) " ( ) ( ) " -, 3 % ( )% ( ) % ( ) F."% &%1% 11 dd d d 0 "# 3 % ( ) " ( ) B
., #" 3 % ( ) " ( ) I )1 1 / /0,11 U"/ WR 3 % ( ) " b ( ) G # ## % - " 1, % "#R/, 1 1. 1 % -# /" 1 3 " ( ) M R ( ) ( ). "/ "# 1 A083 R κ " ( ) κ κ κ κ κ κ κ κ /% % % O"M BP OKF FP 4 -# / κ κ κ κ κ κ
!"#%& '( 3((*3)./ #- J- 2 ) 2 I 2 & 2 K % / #, )11 - / # 4T *,/ # 1% A %1 0 2 ( 2 ) & ( 2 ) % 2 ( 2 ) & ( 2 ) " 13 φ ) ( )2 R φ ) ( ) 4 ) 3 φ ) ( )) φ ) ( ) φ ) ( )) / #0 3 φ ( ) ) φ) ( ) ) φ) ( ) Iφ) φ) ( ) ( ) φ) ( ) Iφ) ( ) φ ) ( ) φ ) ( ) F
B "T / #1 11 3 ( ) ( ) ( ) ) ) ) I φ φ φ %4 3 ( ) ( ) ( ) ( ) ( ) ( ) ) ) ) ) ) ) I I φ φ φ φ φ φ ) 1 A 0 1! φ ) ( ) % / # ( 1 3 ( ) " R/0 1 10 3 " ( )& φ ) ( )Iφ ) ( ) φ ) ( )Iφ ) ( ) % /0 04 2 3400*2:((*3);."% "#( 4/0, / # O7ZGIP3 2 2 4 2. 2 2 4 2. 2 2. 2 F R"%2 % %% R 41 2 2., / "% % % 1 3
2. 2 2. 2 4. 2 4 2. 2 4. 2 4 4. 2 ( ) 4 4 4 ( ) B 2 &X 4 1 "% 2 A 1 0 %3 2 φ ( ) 0 2,/ # 4 2 )1 0 3 2 φ ( ) 4 φ ( ) 4 2 φ ( ) # 3 2 φ ( ) 4 2 φ ( ) 4 I 4 φ ( ). 1 4 1 3 R/ 13 " ( ) G ( ) φ ( ) 4 φ ( ) 4 φ( ) " M %( 1 /14 I
) * & * 0 / # 1 T, 1 - ) 11 1 T % / # 1 % 4 1T%1 # A1 1% J / #11 1 1 # % " U 1W # *1 3 a 2. a2 a 2. a 2 4 a 2 K a 2 a R 1 A 1 2 1 3 2 2 b b 2 e e Ζ ( ) 1T 1 T 10 3 Ζ ( ) 1T 2 b 3 Ζ( 2 b ) 2 b R 1 1 T U W # )11 1 %3 G
A% 3 Ζ( 2 b ) b Ζ( 2 b ) b Ζ b ( 2 ) 2 2 b 2 F % /9%% %/9 "#9 () Ζ ( ) Ζ a2 ( ) ( ) D 1 T 1 2 b % / # 1 " 1 3 D ( ). D ( )( ) B D ( ) (. D ( ))4 D ( )( ) % 1 1 D ( )8D ( )1 3 D D J ( ) (. ) ( ) ( ) (. ) 4 D ( ) ( ) ( ) D ( ) I R A 1 1 1 3 D ( ). D ( ) b b G ( ) (. ) b ( ) M 4 D ( )( ) M
) "%D ( )40 J ( ) 1 1 J / #"#1 3 ( ) b. 4 b. 4 4 b. ( ) J ( ) b ( ) b ( b. ) b ( ) ( ) K K
, - '&.'. 2 # 1 / # ( 1 0 # % / # 1%R#, 1 # 7% -4 " ), / # 1 4 #0" 00-, 1% 3!00 0? / # "# 1 % F # 1% 3 R. 4 2. 2 2. 2 4 2 2. 2 4 2 2
!? " % 1 1 / #, # 3 ( ) b. 4 b. 4 4 b.! ( ) b ( ) b ( b. ) b ( ) A "#.//-6 % % "% 1 3 (. ). ( ).4 - " 0 / # 1 %.- 13 - (. ) (. ) ( ) ).. (. ) -4- E. ( ). 4 2 -. # 3 R # - 3 -.. b - - b a. b ( ) - 01 1! ( )
b. ( ) 4 - ( ) - b. ( ) - ( ) - 4 b b b. ( ) - 4 1 1 -,! ( ) b b b. ( ) - 4 b. ( ) 4 4 b. ( ). 4-4 % 0 3 4 4 4 4 4-4 4. { }13 ( ) ( ) ( ) ( )... 4. 4 4 - # 3 -. b. - b - 4 A% 3 ( ) ( ) a 4 4 4 4 - - 4-4 1 ( ) ( ) a a - 4-4 4 1 1 03! ( ) b b b. ( ) b 4 b b. ( ) 4 4 b. ( ) b
R4-4 )!%4 3!( ) b( b. b ) 4 b ( b. b ) 4 b 4 b ( b. b ) b - b % 1 f 00.!00 0? / # "# 1 % F # 1% 9 3 R 2. 2 2. 2 4 2 2. 2 4 2 2 F. B 4 I G!?.4 - % 1 % 9 0 / # % %. 3.- 13 (. ). ( )
(. ) (. ) (. ) ) - # 3 R -.. b - - b a. b ) ( - ) - 01 1 3 4 (. ) 4 - (- ) (. ) - (- ) 4 - ( - ) (. )- ) - ( ) ( ) b 4 -. b 1 1, 1 3 ( ) b.. ( ) 4 ( b ) 4 (. b ) b! R4 4 -. 3 4 4 4 *14 " - 4 4. { }. # 3 -.. b - - 4 b 4 b 4 b R 1 4 b - 4 ) 1 % 3!( ) b( b. b ) 4 b ( b. b ) 4 b 4 b (. b ) b F
B b - f 041-( A"% /%. 1% 1 % 9. 1 % 13 2. 2 2. 2 4 2 2. 2 4 2 2. 1 B3... 1 3 F3 *,. 1. 1 3 4 4 M
)1. 1 3 G3 # 0.3,.,,2 ; " " % # 0 / #! 1 4 % "% -/ # 0 0!00 0?/ #"#1% F 04 #1% 3 3 3. 2. 2 2. 2 2 2. 2 2 2 K a. F I
!?.1% 1" 3 2. 2 2. 2 4 2 2. 2 4 2 2 % 04 % 4. "/ "# R 4 # 4 % 4 2 % 4 4 1. 2 b 4 2 %3 2. 2 2 b % 2 b 3 ( ) b 2 b 4. 4 *1 b. 4. 4 2 b 4 4 2 3 2 b. b b 2 4 4 2 ( ) " 2 2 b ) -4-1 b. 4. 4 ( ) " 1 2 b 4 4 2 1 4 b 4 f. 1%! 1"!00 0 #? / # "# 1 1 2 # 0!?1% 2 1 3 G
2. 2. 2. 2. 2 ( ) ( ) ( ) 1. 3 2 ( ) R 2 1-2. 13 3.... 2 % -4-# / # f ( ) ( ) M
/ - 0. &, *33,.. 1 % 1 "! 1 J / #%12 %"-/ #"#4 A1 11 %% 1 -# / # # 2 3 2 3 b 2 "%-/ #,14 1 # 3 R 2 2 4 2 F F F ) 11 % /% 1 % F "% -/ #,3 a. 4 % F3 2 ( )2 4 2 2 FF FB 2 4 2 K
% 140 F R2 1, 1 3 D ( ) ( D ( ) J ( )) ( ) FI D ( ) a ( D ( ) J ( )) 4 D ( ) ( ) R0 1 #1 3 2 D D 2 ( ) D ( ) J ( ) ( ) ( ) D ( ) J ( ) ( ) ( ) D ( ) 403 D D ( ) ( ) ( J ( ) ( )) ( ) ( a ) ( J ( ) 4 D ( ) a ( )) A %3 a %% 3 ( a ) a a a a a FG FM ( b ) b b b FK "#, 1 3 ( ) ( ) ( a ) J ( ) 4 D ( ) a ( ) J I ( b ) b b "% 03 J ( ) I b ( ) ( ) ( b ) 4 D B B ( )b ( ) B F
#0 FG 3 D ( ) b ( ) J ( ) ( ) 4 ( b ) J ( ) 4 ( b ) 4 D b b ( )b ( ) ( )b b ( ) ) 40"%-/ # 1 3 J ( ) ( a ) 4 ( a ) J ( ) 4 4 ( a ) J ( ) a a ( ) ( ) I ( a ) ( ) B 11 "% J ( )b ( ) ( ) /9 # % 4 4 * 1 9 b b /9 3 : /99 b : b : : : /99 b : b : b : : A 1 b 1 3 b : { b b : } BF * 0 B ) 1 0/9 b 3 J ( ) ( ) ( )3 { a a a ( ) ( ) } { } J ( ) ( ) ( )3 { a a a ( ) ( ) } { } 8 J ( ) ( )3 a #O"MBF-BBP 0 G { a } { } F
% 1 1 3 Ζ b : J ( ) : Ζ ( : ( )) : A % -4-1 : : 8 * / # "# -/ # " -/ # 1 ; ) 11 % # 0 B -# / # 1 3 J ( ) ( ) ( a ) 4 D ( ) a ( ) I a BB 1%4 1 % 3 4 a BI 4 R4 b # / # B A% 4 D ( ) 3 D ( ) ( ) ( ) ( ) ( ) J 4 D a a BG 4 D 4 D *, 3 ( a a ) a K BM K b b b BK 3 a a J ( ) ( J ( ) ( ) K 4 D ( ) ( )) I ( a I ) # FG3 F
F D ( ) b ( ) J ( )4 D ( )b ( ) ( ) I A% 3 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) D 4 4 K I J 4 K I J I J a a a a a a a a a a I ) 1 3 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 4 4 I J 4 4 K I J I J a a a a a a a a a a a a I 0 / # 1 1 4 0 - " -4- #. % % 0 U"/W % " & 0.3,.,,2 % " 4 # 4 / #. - % A 1 11 1 3
: : : : : : IF ) 11 2 % # 1-3 : : : : : : ( ) : : : % -4-# / # : : : ( ) ( ) ( ) IB FF
3,.,0(),0,.,04433(,." 0 "% 1 / #"# " / # " 4 " 4 / # J"# 2 1 J %- % -4-1 / & ( ) * 1 1 4 / # % " " 0 / # "# 0" / U -" W 1 " % % 4 "% " / / # 0# 4 1 / # J "# 2! J / # "/% % "1 4 / #%% %0# "/% %/"# / #"# FB
'! " % / # /% 0 Z " 4 "% 0 / # 4 /OKFP/ # 4 - / # 0/ # E ) # 4 / #10 / # J / # E 0 / # E "L %/ # % "% #, - 1 # "1 S )11 E / #,1 3 * * R / #* / # % 4 1 E 41 % / #,/ # 3 * 3 3 F b U W { } * A%,4 1 % b 1 3 FI
a a B. U11 W 1 ) "" % / # 4/ # / #1 %3 ( ) I / # # 2 %# 04 - ) % %!! A##,,-.,. 1 S / % # 1 111. # 060 b 1 3 a a ϕ O P G % # 1 3 θ ϕ M θ K # 0 / # 3 θ ϕ ϕ ϕ # 0 0 2 13 2 2 ( ),! 3 FG
( a a ) - 24"% % % 1 1 ) 11 4 % θ ϕ θ %-, ϕ )1 θ 1 4 # θ #4 % % % - 11 *1 # 0 #" " %4.*04 "#E # 4 ""/ #1 3 2 J 4 % & 1 3 &( ) F / # *1 # 3 3 J B I # #/ "% 3 ( ) J ( ) G FM
( ) # 0# 0% " 3 ( ) J M ( ) ) 0 1 # / # 3 J ( J ) J ( ) J K ( J ) ( ) %# 4 A% # " % 3 J ( J ) J ( ) ( ) J *4 4!3 J ( ) J. %4!# -4- % -, 4 )11 % " ( ) J J J % 4 J ( )."% 0 1 J 3 : 1 : : : & : 1 : ( ) 3 1 : : 1 : FK
3 & ( ) ) 1 % % / # 4 # ) 1 " " J 4 0 3 & J ( J ) ( ) 2 # "0 3 3 J ( J ) ( ) J J ( ) / # 3 1 : & : 1 &( ) & : ( J ) J ( ) J ( J ) ( ) J #.." J A & ( ) B
F 4! J ( J ) J ( ) J A 3 ( ) J J # 4-4- 3 ( ) P O P O P J 4!4 &;M F3 O : 1 : : : & : 1 : ' J ( J ) 4!4 1 B B
'! 1 ", 4 " % 0 O KI FP * #4 #! % " # A 3 2 2 0! 2 ) 0 "! 4 4.! / 3 1! a ϕ a O 0 43 θ ϕ ( ϕ ) P ϕ F. # 0 4 # 4 1 " ) 11 2 % θ 2 0 ϕ 0 ϕ %! 0 # / # 14! # 0 0! 2 1 2 2 B B
,!!! 3 a a - I ( ). / # # 11 # 0 #" ".*04 " 1 3 4! -,1 % 10 4 T3! 3 g 4! 0 3 ϕ ϕ ϕ ϕ ϕ ϕ # / #4 / # 3 θ ϕ ϕ ϕ F A " 1 # 1! %! 4 / #3 3 B B
) '&.' #!*33,.! 1 / # % 0% 0 1 J A/ # " % / #, " % / # 4 1 J 3 &( ) G " %/ # / # 4 0 / # / %. %/ # 4 ( 1 1 J % 1 4 1 ) " 4 4 1 /0 "# J, 1 1 "# 4 "# 10 4 / #"#/ J "%1 13 R & ( ) & ( ) M % " " / # %# 0 ) 11 11 4 0 # % # 4 " %1%# " / # 3 2. 2 2. 2 2 2. 2 2 2 BF
03 R. 2 ( ) ( ) { } {. } { } # / #"# %% 1 IB #! 1 4 / #"# /- 1 "%. / 3. 2 ( ) 2. 2. 2. 2 ( ) 2. 2 2. 2 ( ) ( ) % ( ) ( ) K # 4 0 % " 3 ( ) : : ( ) 2 : ( : ) ( ) : ( ) : : % 4 % 1 X 1 % # % % 2 # 0 % " 4 / # # 11 "./ #% 3 : BB
R. : : 2 ( ) : ( ) : : 2 : ( : ). 2 2 : ( : ) ( ) 2 : ( : ) ( ) 2 : ( : ) : ( : ). ( ) ( ) : : 2 -# 2 2 ( ) ( ) : ( ) # " 4! %% % 4# % % #, A,(,B # B,0 (060 )0% % 4 * % % 13 *1 2. 2. J 2 ( ) ( ) ( 2 ) ( ) 2 D b ( ) BI
3 a... 0, 1 3 ( a a ) J (. ) D ( ) a F % " 3 ( ) J ( )D ( ) B ) 0 / # # 3 J ( J ) a J a ( D ). J a ( ) J D ( J ) a a a ( D )( D ). D ( ) D a a ( J ) a ( D ). ( ) I # C60433(, 4 / # J ( J ) 4 J ( J )! 4 - # - 4 J. # 4 { }X " 3 ( ) J J J G J ( D ) 3. - 2 : : : "/ "# 3 BG
( ) : 2 : : 2 : : : ( ) J : ( ) 3 ( ) ( : ) : ( ) : & (: : ) : R& ( )1 # ( ) D D - M : K : 2 ( 2 : ) : : 1% 3 D 2 ( 2 : ) : 2 ( ) ( 2 ) : : F ( ) - 2 : : /% ( ) 43 ( ) ( ) 2 : 2 ( ) : : ( ) ( ) : # 43 : F : F ( ) : : F :. / # 1 3 J D 2 : : : 3 BM
1 # : ( ) & :: ( ) ) 1 2% / #%1 # 4 4 3 2 2 ( 2 ) 2 ( : ) : F A% " " ( ) A "3 2 2 2 12. 2 3 ( ). 2 2 2 ( 2 ). ( ) ( 2 ). 2 ( ). ( ) ) 1 % 13 *, b R ( ) J ( ). 2 2 b (. ) D 2 ( 2 ). ( ) FF ( ) ( b ) 4 ( a a a ) J (. ) D ( ) a ( a ) J ( ) ( ) FB FI A " "3 2 ( ) 2 : : o o A BK
2 2 Aσ 2 σ. σ 2 σ σ σ. σ 2 σ σ & ( σ) 2. 2 σ σ σ σ σ F. 2 σ σ a o ( ) J (. ) D ( a ) a 2 % " %% U W " 1 σ 4 * 1 % & ( ) 11 / " #.*04 " " : D : ( : ) D D 3: 3 D 13 : D 3: D 3 { : :: : } 4 3 104T1 3 : ( ) : J 1 & (: : ) : / # ( ) ( ) F & ( ) σ 1 : I
( J ) D ( J ) J D ( ) b J b b D ( D ) b ( J ).. D D ( ) b J ( ) b ( ) b ( ) b J D b. # b. b b. Z.1 2 2 ( ) 3 ( ) b 2 2 b F 4! D D B 4! 2 ( 2 ). b. ( ) J ( ) ( ) D D ( ) D D J ( ) 3 3 ( ) J ( ) J b J 3 3 3 ( ) 2 2 ( ) ( ) ( ) 3 3 D D 3 3 J ( ) ( ) I. " 2 ( ) 2 : : A o 2 2 o Aσ 2 σ. σ 2 σ σ & ( σ) F 2. 2 σ σ σ σ I
o & ( ) a o ( ) ( ) ( a ) a J. D 4! D J D 2 J 2 I
, '&.'!*33,.! 1 4 / # /% % 0% U 0W J 2!! ) %/ # /%13 2 ( 2 θ) FG & ( 2 )* R * θ # "" # θ% #% *# #1# # 1 " 1 / # /% 1 S 0 * 1 3 2 ( 2 ) θ FM & 2 ( ) #41 ( ) ( ) FK )11 # 40 A" %#! 1"T 1 3 2 ( 2 θ ) B & ( 2 ) %! 4 "T ""# θ % # A% #% %4#011 % # θ 0. I
/ # "# 4 1 " 3 3 2. 2 ( ). : 2 : ( ) : ( ) : ( ) A1 2 42 *# 1! 3 J D ( ) ( ) ( 2 ) ( 2 ) B % B 3. b.. B 0, 1 3 ( ) J (. b ) D ( ) BF # 0% " 3 ( ) J ( ) D BB ( ) ) 0 / # # 3 IF
( ) J J ( ) J D. b D ( J ) ( J ) D J ( ) D ( ) D ( ) D D ( ) b.. b J ( ) BI.*04433(, "" 3 3 / # 104T13 ( ) ( ) ( ) / #1% 3 J ( J ) J ( D ). b J ( ) D ( J ) ( J ) D D ( ) D ( ) D D ( ). ( ) b.! 2 A. 2 ( ) A. b ( ) J IB
2. : : : 2 ( ) : ( ).!! 2 11 F 4! / #3 J ( J ) J ( J ) 8 B,B?* #/ # -! 4 " R / #,B?. # / U - " W% II
#/. ( 0(),0"33(, ) % 1 1 "" -! " "%*DKI- " 1 / # F 1 "" 0 U 0 1 W73n4sid.m"- armax.m oe.m "% /&-Y 1F 3 ( ) F 1 104T %/ # 1 1 1 2 # 1 % " " 1 N F %" "!/ # % "%- *#.1 " IG
*1 "% # / #IB9 IT J 7 011 / # " " " / &-Y 1 F %# B # " " % " 4 4 *# ) # IM
) % # 1 2,.,B,(,B Q "" / # # % % 8 8 11 M M M3! B 1 1 ".) 1)A " / 01 O'MGP 1 # 11 " 2 % " " 0 "% *#A# IK
*##A# G
*#A# # / # "" 0 "% # 0/,0(3(%0.,(*3) #/ #1 1# - /3 ( ) F R () 1 %% %# - % / #0) # O "G "MP G
% - / # % OS7ZKP3 : : : : F : : % / # 4 / # "# " % 4( 1 )" / # # 3 R10# 0 c B 8 8 8 8 0 1OMGP &! 4 J B7 * " 0 / #% O) "IP3 : : : F F # #% / # 1 3 9 F B 9 R % ", O!KKP G
*#&0 #F F 1 J BN" "% # " 1 4 1 11 " ' F I 1 % 80 #11 cmkbn G
*#'0 # "" - 1 J BN" "% "" - 1F G # "- "# OIP 1%" - 4 # 0 4"" 1 # B7 A 1 ( N *? 6 BJBN MG B - GM GB FF,-.,# F 0 0 "% 1 % " " 1 %N 1/ 4"- GF
1 # 1 # 1 0 4% F. #!%4 0 0 / # 11 0 1 4 11 %1 4%/ ", " " / 4 "% O KIP A ( % % 1 % % % 11 / 1 / # G GB
0. 0 ; " " 4# 1 / # 0 1 % 4 " % 11 4 1 #0 / # /, % / # % 1 ( - # # "# 4 " / # 4 ( 1 4"T1 - "" 0 X" 1 %/4 1 # / # 4 " O."MKP ) # % " "04 "0 1 ( % % % 8 1 /0 4-0 1 % % # 4 0#% 41 %# %1 / #4 1 " 4 1 / # - 1 # " " # 1% ) # 1!0U W 3-0 1 % #4 0# 14 - - /1%# 4 0 " % 4 4% - ) "! 1 % "!4 0 X0 GI
-.0*,4 O KBP O7MP O7ZIBP O7ZGIP O7ZGIP O7ZGIP O7GFP O."MKP O."MKP h/ 1 i. KKB 7 h 1 1 / C /i- G IG-MFKM 7Z"11 &.%* 7. ) "./KIB 7Z L h( &. "/i. IG-GIKGI 7Z L h/ *11 & /i-& IF I-GKGI 7Z L h' 1 * 7 T i C&) IBK-BKGI 7. h7 / 3. 1 / / "/ i..-k FF-FMKGF." 7 h 1 - / 3 " EiC FK -KMK." 7 h A ) A ) 1 - ic FK BIK-BKFKMK O."KKP.". L% &4 ) 01 / AKKK O."P O."P O."KMP O."ZGKP." 6!YZ h 1 " 1. * - " 7/ i-).%, % F%J%4### 7..". 6 AY) h( S) " 1. / 1 AS? i %- FK FG-I."/ L h "." T 1 * 7' i % ; FB B B-BGKKM."Z * h' 17/ Y " i..-f IKFM-KB KGK GG
O."KFP O.MP." D AY) h? / 1 6" 1 * i %- F B IM-GKKF." A ) h*/ T 1 ' ( i%.7c E, K GG-KM O*GFP * A ht "/ 1 7 */ / i%.7 C BG-BB KGF O*MKP *6 " S h -% "Y " 1 L " 1 7 / 1 i- I -IKMK O) "IP ) "/ & h? / 1 / 6 / "i ##. F%,&F % -.AjI ' F-K I K- O)MP O'KKP O'P O'GKP O'MP O'MP O'MGP O'TMP ) ) h7/ Y "6 - i..-m -BKM ' L * 7 ( " A h 1 1 7 /! L " i. FF IKKK ' L * 7 ( " A h 1 1 AiC- FK-BB ' h Z " 1 ' " T 1 6. -/ i..-f BG-BMKGK ' -./ * h "0 1/ / -i).%, % - B-BFKM ' h " ' )0i % F.- M BBF-BG KM '" '! h 1 1 7 / i C FB FB-FGKMG 'T" ) h"1 7/ "/i%.7c M IIF-IBMKM GM
O&MKP O&P O&GKP O&KKP O& "BP O&P O6MMP O6KKP O)))KP O)))BP OMFP OGKP OSP OSBP & E D h ' 7 i-%.%gf-gfkmk &Z & 7 ) h 7"/ / 1 i%- MB-BM & ) h 1 ' 1 6 / i. F F-FKKGK & & SZ A S h)11 " 1 ( / 1 i %- FG F-BGKKK & " h 1 1 6 / % ( "i. B BK-BKB &T. 7/ ) h 1 1 6 L i). & " 6 ha 1 1*// 7. ' i- B IFB-F KMM 6 STZ/ 9 % F,;E, 7.,,&SYA"KKK h / 1 1. *i. G GKK h / 1 i. B B Z "TZ6 h7/ 1 /( S ) i..-k MGFI- GFKKMF L. *A KGK S SZA "Y( h7 1 17 / i %- B FMF-FKK S SZA h7 1 1( -6 / i %- B MGGG-GMGB OS7ZKP S7Z6 "Y( h 7' i %- F I-FIKK GK
OSIP OSP OS"MBP OSKP OSGFP OSGBP OKFP OKP O&P OGMP O!MP O!KKP O!P O!BP OMBP S ' & hl -6 / *( S.11 i%- L II S7 Y&. L%?& *, 7.L.62, SYJAA" S" AY) h-( ' / 1 i. F %,&F % - A- IFFB-FBBKMB S A * h " " - // 1 i%-7k-fkk S ht 7T 1. / i-.% &MF-MFKGF S h7 T 1 - i %.7C FMG-MFKGB "-'. % 9L 6#KKF L ) h.( / 1 '. i- & 4 6Y BKI-IFKK &) / h7" "% 1 6" AY 1 Y " /i7;%4 KM-KMI Z. S h")0 %1( 1 / i..- I K-KBKGM! k k &- *" AKM! % && ) A 6 AKKK! h7z-70 1 - i 7 &7 M-FI! ( h& ) 3/ 1 i. B BFG 7 h - A 1 / A 3 * / i C F -MKMB M
OMBP OMGP OIGP O "KP O "KIP O KMP OP O TGKP O"GP O "MP OMGP OKFP OKIP OKIP O FP 7 h - A 1 / A 3 " / ic F K-FFKMB 7 l)0 * 1 / 1 -/ lc% % M MK-KMG * h. ' 1 / i.k-kkig "Y( S ha ) 17 i-b-bikk "Y( h( ' " i %- L G-KKKI D. ' h 1 1 7 / 7/1i-.%%-IK-IKKM D. ' ha ) 1 " 1 17/ i-.%%-gi-m T & ) h 1 ' 1 6 / i..-f F-FKKGK " 6 - " ) IAKG " ST!L hy17/ "/ i % F7F.- IM- IMMKM -./ * h' ( - T - 0 1 - * - / ic FB BGG-GMGKMG & h)0 A 1 ' i %- F FMGG-MMIKKF & h 1 3 Y 6 / "i %- FF I-G KKI & h ( ' Y " 7 / i %- FF K K- KKI h E 1 ( 6 / "i. FK -MF M
OP OAZMP OAGMP O KFP O"MP O"MP O"/ZMKP OGKP OIP OKBP OP O(KFP O(KBP 1." h ( / 1 7 * L i-;3 %- FM -K AZ A/ ' h * 1 / 1 i %.-M F- KM A & h. ' 1 7 J i..- FBKB-IKGM 6 h 1 17.'i- &M-MMKKF " L 9% & & 3J".,,& " " 6Z / A KM L 3 YYY!" Ja"J JZ1 " T &3"& 9% S A"./KM "/Zh' i.%%-7f-kmk ) * ht "/1* -/ 3A "7.i %.-I F F-BIKGK L ) "/ & l " j 1 / # l.1 '"j %-).I70'. 6 AY ) h 1 1. / 6" 1 * i %- F GG-GBKKB Z ( SZ A S h 1 1-7/. i %- FK GB-GI ( " A * 7 hf*3 " 1 " 1 1. * - " / i. GB-KKKF ( " A * 7 h 1/ " 1 " / 1 "i. MB-MIF KKB O(KIP ( " A * 7 %, L% SYA"KKI M
O(KKP O(P O(P O("KFP O(KP O(KBP O(P OL P OL KIP O"KMP O"KMP O"KKP ( ( (".". h 1 1 7 %i-. MM-MFKKK ( ( (" h 1 1 7 / 7 "% % T ic GF MMF-MI ( ( 9% N.%;%,.,,& A"* " /1Y (" h 1 1 "* A 1 ' 1 - * i. I-GFKKF ( ha1 1 7 / 1 "i- & )." // GIK-GKK ( h- " 1 " 1 1 - / i. MB-MBKKB ( h. 7 & 6?&.,4,4 )-?., i A"* " /1' L 7T h( --7 7" 1. / 1 6" '%i 7?*&&1 B BF-FF L YZ * (" h 1/ L / 1 "i%- BB- BMKKI "? h' 11 ( S) 3)" ( /i. 6 I -IKKM " E ( h A 1 ( S i7&,7 G BG-F KKM " 6 l 1 1 7 / l-.%%-mk-kkkk M
Resumé en français / #! 9 / # - %0 / #-/ %0 # / # "# 1 - ( 4"T1 1 " 1 "!% 0 / # 4 1 / # % 0 0 % % 1 E E 0 1 / #"" 0%% % "0 "% 1-( / #76# 1 6 Resumé en anglais? / "1 Z1/ Y""Y / / "/ 0 / Y " " 0 1 ( "" / 1 " Y / 0 " 1 1 1 / / " 0 1 Y % E E 0 / 1 1 / " / 23;( 67/ 6 / 1