Sliding mode control of switched linear systems based on common Lyapunov function

The sliding mode control methodology for a class of switched linear systems with the immeasurable states is presented. A reduced-order observer is designed, which guarantees the stability of observer error system under arbitrary switching in a common quadratic Lyapunov function framework. Based on the estimated states, a sliding mode control law is synthesized to enforce asymptotic stability for the individual closed-loop modes, and to provide an explicit characterization of the corresponding stability region for each mode. Moreover, a set of switching laws, which are based on the evolution of the estimated states, are then designed to guarantee asymptotic stability of the overall switched closed-loop system. A numerical example is provided to demonstrate the effectiveness of the proposed approaches.