New Development in Quadratic L 2 Performance of Switched Uncertain Stochastic Systems.

Global quadratic stability and L 2 performance in probability (quadratic stability and L 2 gain γ in probability: abbreviated as GQ L 2 (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 GQ L 2 (γ) -P, it is shown that if there exists a convex combination of subsystems achieving GQ L 2 (γ) -P, then a state-dependent switching law, based on the convex combination of subsystems, is proposed under which the switched system achieves GQ L 2 (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. [ABSTRACT FROM AUTHOR]