Quadratic ℒ2 Performance of Switched Linear Uncertain Stochastic Systems

We study global quadratic ℒ
2
performance in probability (quadratic stability and ℒ
2
gain γ in probability: abbreviated as GQℒ
2
(γ)-P) for switched systems which are composed of a finite set of linear stochastic subsystems with norm bounded uncertainties. Assuming that no single subsystem achieves GQ ℒ
2
(γ)-P, we show that if a convex combination of subsystems achieves GQℒ
2
(γ)-P, then we can design a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched system achieves GQℒ
2
(γ)-P. A numerical example is provided to show effectiveness of the proposed approach.