THÈSE DE DOCTORAT Ecole Doctorale « Sciences et ...

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204 Annexe D. Théorèmes du p<strong>et</strong>it gain pour des systèmes paramétrés { |ω2 a (x 2(t))| ≤ max β 2 (|ω 2 (x 2 ( t 2 ))|, t } 2 ),γω 1 2 (‖ω 1(x 1 )‖ [ t 2 ,t)),γu 2 (‖u 2‖ [ t ,t)) , 2 { ≤ max β 2 (2β 2 (|ω 2 (x 2 (t 0 ))|,0), t 2 ),β 2(2γ ω 1 2 (β 1(|ω 1 (x 1 (t 0 ))|,0)), t 2 ), β 2 (2γ ω 1 2 (γu 1 (‖u 1‖ [t0 ,t) )), t 2 ),β 2(2γ ω 1 2 (γωb 2 1 (α 2(|ω b 2 (x 2(t 0 ))|))), t 2 ), β 2 (2γ ω 1 2 (γωb 2 1 (ηω 1 2 (β 1(|ω 1 (x 1 (t 0 ))|,0)))), t 2 ), β 2 (2γ ω 1 2 (γωb 2 1 (ηω 1 2 (γωa 2 1 (β 2(|ω 2 (x 2 (t 0 ))|,0))))), t 2 ), β 2 (2γ ω 1 2 (γωb 2 1 (ηω 1 2 (γωa 2 1 (γu 2 (‖u 2‖ [t0 ,t) ))))), t 2 ), β 2 (2γ ω 1 2 (γωb 2 1 (ηω 1 2 (γu 1 (‖u 1‖ [t0 ,t) )))), t 2 ), β 2 (2γ ω 1 2 (γωb 2 1 (ηω 1 2 (γωb 2 1 (α 2(|ω b 2 (x 2(t 0 ))|))))), t 2 ), β 2 (2γ ω 1 2 (γωb 2 1 (ηω 1 2 (γωb 2 1 (ηωa 2 2 (β 2(|ω 2 (x 2 (t 0 ))|,0)))))), t 2 ), β 2 (2γ ω 1 2 (γωb 2 1 (ηω 1 2 (γωb 2 1 (ηωa 2 2 (γu 2 (‖u 2‖ [t0 ,t) )))))), t 2 ), β 2 (2γ ω 1 2 (γωb 2 1 (ηω 1 2 (γωb 2 1 (ηu 2 (‖u 2‖ [t0 ,t) ))))), t 2 ), β 2 (2γ ω 1 2 (γωb 2 1 (ηω 1 2 (m))), t 2 ),β 2(2γ ω 1 2 (γωb 2 1 (ηu 2 (‖u 2‖ [t0 ,t) ))), t 2 ), β 2 (2γ u 2 (‖u 2‖ [t0 ,t) ), t 2 ),β 2(2m, t 2 ),β 2(2α 2 (|ω b 2 (x 2(t 0 ))|), t 2 ), β 2 (2η ω 1 2 (β 1(|ω 1 (x 1 (t 0 ))|,0)), t 2 ), β 2 (2η ω 1 2 (γωa 2 1 (β 2(|ω 2 (x 2 (t 0 ))|,0))), t 2 ), β 2 (2η ω 1 2 (γωa 2 1 (γu 2 (‖u 2‖ [t0 ,t) ))), t 2 ), β 2 (2η ω 1 2 (γu 1 (‖u 1‖ [t0 ,t) )), t 2 ), β 2 (2η ω 1 2 (γωb 2 1 (α 2(|ω b 2 (x 2(t 0 ))|))), t 2 ), β 2 (2η ω 1 2 (γωb 2 1 (ηωa 2 2 (β 2(|ω 2 (x 2 (t 0 ))|,0)))), t 2 ), β 2 (2η ω 1 2 (γωb 2 1 (ηωa 2 2 (γu 2 (‖u 2‖ [t0 ,t) )))), t 2 ), β 2 (2η ω 1 2 (γωb 2 1 (ηu 2 (‖u 2‖ [t0 ,t) ))), t 2 ), β 2 (2η ω 1 2 (m), t 2 ),β 2(2η ωa 2 2 (β 2(|ω 2 (x 2 (t 0 ))|,0)), t 2 ), β 2 (2η ωa 2 2 (γω 1 2 (β 1(|ω 1 (x 1 (t 0 ))|,0))), t 2 ),
Annexe D. Théorèmes du p<strong>et</strong>it gain pour des systèmes paramétrés 205 β 2 (2η ωa 2 2 (γω 1 2 (γu 1 (‖u 1‖ [t0 ,t) ))), t 2 ), β 2 (2η ωa 2 2 (γω 1 2 (γωb 2 1 (α 2(|ω b 2 (x 2(t 0 ))|)))), t 2 ), β 2 (2η ωa 2 2 (γω 1 2 (γωb 2 1 (ηω 1 2 (β 1(|ω 1 (x 1 (t 0 ))|,0))))), t 2 ), β 2 (2η ωa 2 2 (γω 1 2 (γωb 2 1 (ηω 1 2 (γωa 2 1 (β 2(|ω 2 (x 2 (t 0 ))|,0)))))), t 2 ), β 2 (2η ωa 2 2 (γω 1 2 (γωb 2 1 (ηω 1 2 (γωa 2 1 (γu 2 (‖u 2‖ [t0 ,t) )))))), t 2 ), β 2 (2η ωa 2 2 (γω 1 2 (γωb 2 1 (ηω 1 2 (γu 1 (‖u 1‖ [t0 ,t) ))))), t 2 ), β 2 (2η ωa 2 2 (γω 1 2 (γωb 2 1 (ηω 1 2 (γωb 2 1 (α 2(|ω b 2 (x 2(t 0 ))|)))))), t 2 ), β 2 (2η ωa 2 2 (γω 1 2 (γωb 2 1 (ηω 1 2 (γωb 2 1 (ηωa 2 2 (β 2(|ω 2 (x 2 (t 0 ))|,0))))))), t 2 ), β 2 (2η ωa 2 2 (γω 1 2 (γωb 2 1 (ηω 1 2 (γωb 2 1 (ηωa 2 2 (γu 2 (‖u 2‖ [t0 ,t) ))))))), t 2 ), β 2 (2η ωa 2 2 (γω 1 2 (γωb 2 1 (ηω 1 2 (γωb 2 1 (ηu 2 (‖u 2‖ [t0 ,t) )))))), t 2 ), β 2 (2η ωa 2 2 (γω 1 2 (γωb 2 1 (ηω 1 2 (m)))), t 2 ), β 2 (2η ωa 2 2 (γω 1 2 (γωb 2 1 (ηu 2 (‖u 2 ‖ [t0 ,t) )))), t 2 ), β 2 (2η ωa 2 2 (γu 2 (‖u 2 ‖ [t0 ,t) )), t 2 ),β 2(2η ωa 2 2 (m), t 2 ), β 2 (2η u 2 (‖u 2 ‖ [t0 ,t) ), t 2 ),γω 1 2 (β 1(β 1 (|ω 1 (x 1 (t 0 ))|,0), t 2 )), γ ω 1 2 (β 1(γ ωa 2 1 (β 2(|ω 2 (x 2 (t 0 ))|,0)), t 2 )),γω 1 2 (β 1(γ ωa 2 1 (γu 2 (‖u 2 ‖ [t0 ,t) )), t 2 )), γ ω 1 2 (β 1(γ u 1 (‖u 1 ‖ [t0 ,t) ), t 2 )), γ ω 1 2 (β 1(γ ωb 2 1 (α 2(|ω b 2(x 2 (t 0 ))|)), t 2 )), γ ω 1 2 (β 1(γ ωb 2 1 (ηωa 2 2 (β 2(|ω 2 (x 2 (t 0 ))|,0))), t 2 )), γ ω 1 2 (β 1(γ ωb 2 1 (ηωa 2 2 (γu 2 (‖u 2 ‖ [t0 ,t) ))), t 2 )), γ ω 1 2 (β 1(γ ωb 2 1 (ηu 2 (‖u 2 ‖ [t0 ,t) )), t 2 )), γ ω 1 2 (β 1(m, t 2 )),γω 1 2 (γωa 2 1 (‖ωa 2(x 2 )‖ [ t 2 ,t))), γ ω 1 2 (γωb 2 1 (α 2(α 2 (|ω b 2 (x 2(t 0 ))|)))), γ ω 1 2 (γωb 2 1 (α 2(η ω 1 2 (β 1(|ω 1 (x 1 (t 0 ))|,0))))), γ ω 1 2 (γωb 2 1 (α 2(η ω 1 2 (γωa 2 1 (β 2(|ω 2 (x 2 (t 0 ))|,0)))))),
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N° D’ORDRE 9655 THÈSE DE DOCTOR
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« Tout est déjà dans l’air il
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ix Remerciements Je remercie sincè
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Table des matières xi Table des ma
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Table des matières xiii 5.3.2 Obse
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Contributions 1 Contributions Les c
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Contributions 3 de la zone où se s
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Publications 5 Publications La list
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Notations 7 Notations Ensembles On
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Notations 9 (ou les solutions) de (
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11 Première partie Contributions
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14 Chapitre 1. Introduction véhicu
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16 Chapitre 1. Introduction où x =
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18 Chapitre 1. Introduction Exemple
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20 Chapitre 1. Introduction ment é
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22 Chapitre 1. Introduction 1.3.2 S
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24 Chapitre 1. Introduction CTD DTD
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26 Chapitre 1. Introduction
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28 Chapitre 2. Commande adaptative
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avec ⎧ ⎪⎨ ⎪ ⎩ p 011 (x,u
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48 Chapitre 3. Backstepping robuste
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Chapitre 4. Introduction 69 Chapitr
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Chapitre 4. Introduction 71 Ordonna
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Chapitre 4. Introduction 73 limité
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Chapitre 4. Introduction 75 et d’
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Chapitre 4. Introduction 77 Une ana
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Chapitre 4. Introduction 79 états.
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Chapitre 4. Introduction 81 frag re
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Chapitre 4. Introduction 83 On déd
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Chapitre 4. Introduction 85 frag re
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Chapitre 4. Introduction 87 Lorsqu
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Chapitre 4. Introduction 89 L’id
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Chapitre 5. Conditions suffisantes
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Chapitre 6. Extension des observate
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Chapitre 7. Convergence semiglobale
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Page 163 and 164: Chapitre 7. Convergence semiglobale
Page 173: Annexes
Page 176 and 177: 166 Annexe A. Rappels mathématique
Page 178 and 179: 168 Annexe A. Rappels mathématique
Page 180 and 181: 170 Annexe B. Rappels de stabilité
Page 182 and 183: 172 Annexe B. Rappels de stabilité
Page 184 and 185: 174 Annexe C. Preuve de la Proposit
Page 186 and 187: 176 Annexe D. Théorèmes du petit
Page 230 and 231: 220 Annexe E. Fonction de Lyapunov
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Page 240 and 241: 224 Références [13] K. J. Aström
Page 242 and 243: 226 Références [45] D. Dochain an
Page 244 and 245: 228 Références [78] D. Hristu and
Page 246 and 247: 230 Références [110] D.S. Laila a
Page 248 and 249: 232 Références [140] P. Naghshtab
Page 250 and 251: 234 Références [169] S. Sastry an
Page 252: 236 Références [202] G.D. Warshaw
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