New Development in Quadratic L₂ Performance of Switched Uncertain Stochastic Systems

Global quadratic stability and L₂ performance in probability (quadratic stability and L₂ gain γ in probability: abbreviated as GQL₂ (γ)-P) is studied for switched systems consisting of linear stochastic subsystems with norm-bounded uncertainties. Under the assumption that there is no single subsystem achieving GQL₂ (γ)-P, it is shown that if there exists a convex combination of subsystems achieving GQL₂ (γ)-P, then a state-dependent switching law, based on the convex combination of subsystems, is proposed under which the switched system achieves GQL₂ (γ)-P. Then, the discussion is extended to the case involving state feedback controller gain. A numerical example and the application to DC–DC boost converters are provided to demonstrate the proposed design condition and the algorithm.