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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200 Annexe D. Théorèmes du p<strong>et</strong>it gain pour des systèmes paramétrés<br />
où, pour (s,t) ∈ R 2 ≥0 ,<br />
{<br />
˜β 1 (s,t) = max β 1 (β 1 (s,0), t 2 ),β 1(γ ωa 2<br />
1 (β 2(s,0)), t 2 ),β 1(γ ωb 2<br />
1 (α 2(s)), t 2 ),<br />
β 1 (γ ωb 2<br />
1 (ηωa 2<br />
2 (β 2(s,0))), t 2 ),γωa 2<br />
1 (β 2(2β 2 (s,0), t 2 )),<br />
γ ωa 2<br />
1 (β 2(2γ ω 1<br />
2 (β 1(s,0)), t 2 )),γωa 2<br />
1 (β 2(2γ ω 1<br />
2 (γωb 2<br />
1 (α 2(s))), t 2 )),<br />
γ ωa 2<br />
1 (β 2(2γ ω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (β 1(s,0)))), t 2 )),<br />
γ ωa 2<br />
1 (β 2(2γ ω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (γωa 2<br />
1 (β 2(s,0))))), t 2 )),<br />
γ ωa 2<br />
1 (β 2(2γ ω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (γωb 2<br />
1 (α 2(s))))), t 2 )),<br />
γ ωa 2<br />
1 (β 2(2γ ω 1<br />
2 (γωb 2<br />
1 (ηω 1<br />
2 (γωb 2<br />
1 (ηωa 2<br />
2 (β 2(s,0)))))), t 2 )),<br />
γ ωa 2<br />
1 (β 2(2α 2 (s), t 2 )),γωa 2<br />
1 (β 2(2η ω 1<br />
2 (β 1(s,0)), t 2 )),<br />
γ ωa 2<br />
1 (β 2(2η ω 1<br />
2 (γωa 2<br />
1 (β 2(s,0))), t 2 )),γωa 2<br />
1 (β 2(2η ω 1<br />
2 (γωb 2<br />
1 (α 2(s))), t 2 )),<br />
γ ωa 2<br />
1 (β 2(2η ω 1<br />
2 (γωb 2<br />
1 (ηωa 2<br />
2 (β 2(s,0)))), t 2 )),<br />
γ ωa 2<br />
1 (β 2(2η ωa 2<br />
2 (β 2(s,0)), t 2 )),γωa 2<br />
1 (β 2(2η ωa 2<br />
2 (γω 1<br />
2 (β 1(s,0))), t 2 )),<br />
γ ωa 2<br />
1 (β 2(2η ωa 2<br />
2 (γω 1<br />
2 (γωb 2<br />
1 (α 2(s)))), t 2 )),<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 (β 1(s,0))))), t 2 )),<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 (γωa 2<br />
1 (β 2(s,0)))))), t 2 )),<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 (γωb 2<br />
1 (α 2(s)))))), t 2 )),<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 (γωb 2<br />
1 (ηωa 2<br />
2 (β 2(s,0))))))), t 2 ))<br />
γ ωb 2<br />
1 (ηωa 2<br />
2 (β 2(2β 2 (¯ρ(s),0), t 2 ))),γωb 2<br />
1 (ηωa 2<br />
2 (β 2(2γ ω 1<br />
2 (β 1(s,0)), t 2 ))),<br />
γ ωb 2<br />
1 (ηωa 2<br />
2 (β 2(2γ ω 1<br />
2 (γωb 2<br />
1 (α 2(s))), t 2 ))),<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 (β 1(s,0)))), t 2 ))),<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 (γωa 2<br />
1 (β 2(s,0))))), t 2 ))),<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 (γωb 2<br />
1 (α 2(s))))), t 2 ))),<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 (γωb 2<br />
1 (ηωa 2<br />
2 (β 2(s,0)))))), t 2 ))),
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