Static output feedback control for discrete-time switched linear systems under arbitrary switching

This paper considers the problem of static output feedback (SOF) control for discrete-time switched linear systems under arbitrary switching laws. Based on a switched quadratic Lyapunov function, new sufficient LMI conditions for SOF stabilization are obtained which guarantee a γ-performance of the closed-loop switched systems subject to external disturbances. More importantly, by using Finler's lemma, two sets of slack variables with special structure are introduced to improve the performance and reduce design conservatism. The proposed method can work successfully in situations where the existing methods fail. Three examples are given to illustrate the effectiveness of our method.