THÈSE DE DOCTORAT Ecole Doctorale « Sciences et ...
THÈSE DE DOCTORAT Ecole Doctorale « Sciences et ...
THÈSE DE DOCTORAT Ecole Doctorale « Sciences et ...
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Annexe D. Théorèmes du p<strong>et</strong>it gain pour des systèmes paramétrés 203<br />
γ ωb 2<br />
1 (α 2(η ωa 2<br />
2 (γu 2 (s)))),<br />
γ ωb 2<br />
1 (α 2(η u 2 (s))),γωb 2<br />
1 (ηu 2 (s)),γu 1 (s) }, (D.106)<br />
˜σ m 1 (s) = max {β 1 (s,0),γ ωa 2<br />
1 (β 2(2γ ω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (s))),0)),γωa 2<br />
1 (β 2(2s,0)),<br />
γ ωa 2<br />
1 (β 2(2η ω 1<br />
2 (s),0)),<br />
γ ωa 2<br />
1 (β 2(2η ωa 2<br />
2 (γω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (s)))),0)),γωa 2<br />
1 (β 2(2η ωa 2<br />
2 (s),0)),<br />
γ ωb 2<br />
1 (ηωa 2<br />
2 (β 2(2γ ω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (s))),0))),<br />
γ ωb 2<br />
1 (ηωa 2<br />
2 (β 2(2s,0))),<br />
γ ωb 2<br />
1 (ηωa 2<br />
2 (β 2(2η ω 1<br />
2 (s),0))),<br />
γ ωb 2<br />
1 (ηωa 2<br />
2 (β 2(2η ωa 2<br />
2 (γω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (s)))),0))),<br />
γ ωb 2<br />
1 (ηωa 2<br />
2 (β 2(2η ωa 2<br />
2 (s),0))),<br />
γ ωb 2<br />
1 (α 2(η ω 1<br />
2 (s))),<br />
γ ωb 2<br />
1 (α 2(η ωa 2<br />
2 (γω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (s)))))),<br />
γ ωb 2<br />
1 (α 2(η ωa 2<br />
2 (s))) }, (D.107)<br />
˜σ ω 1 (s) = max { γ ωb 2<br />
1 (α 2(α 2 (s))),<br />
γ ωb 2<br />
1 (α 2(η ω 1<br />
2 (β 1(s,0)))),<br />
γ ωb 2<br />
1 (α 2(η ω 1<br />
2 (γωa 2<br />
1 (β 2(s,0))))),<br />
γ ωb 2<br />
1 (α 2(η ω 1<br />
2 (γωb 2<br />
1 (α 2(s))))),<br />
γ ωb 2<br />
1 (α 2(η ω 1<br />
2 (γωb 2<br />
1 (ηωa 2<br />
2 (β 2(s,0)))))),<br />
γ ωb 2<br />
1 (α 2(η ωa 2<br />
2 (β 2(s,0)))),γ ωb 2<br />
1 (α 2(η ωa 2<br />
2 (γω 1<br />
2 (β 1(s,0))))),<br />
γ ωb 2<br />
1 (α 2(η ωa 2<br />
2 (γω 1<br />
2 (γωb 2<br />
1 (α 2(s)))))),<br />
γ ωb 2<br />
1 (α 2(η ωa 2<br />
2 (γω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (β 1(s,0))))))),<br />
γ ωb 2<br />
1 (α 2(η ωa 2<br />
2 (γω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (γωa 2<br />
1 (β 2(s,0)))))))),<br />
γ ωb 2<br />
1 (α 2(η ωa 2<br />
2 (γω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (γωb 2<br />
1 (α 2(s)))))))),<br />
γ ωb 2<br />
1 (α 2(η ωa 2<br />
2 (γω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (γωb 2<br />
1 (ηωa 2<br />
2 (β 2(s,0))))))))) } . (D.108)<br />
De la même manière, d’après (D.96), (D.98), (D.99), (D.100), (D.101) <strong>et</strong> (D.102),
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