Stabilization and performance analysis for a class of switched systems

This paper investigates stability and control design problems with performance analysis for discrete-time switched linear systems. The switched Lyapunov function method is combined with Finsler´s lemma to generate various tests in the enlarged space containing both the state and its time difference, allowing extra degree of freedom for stability analysis and control design. Two performance measures being considered are the decay rate and the input-output performance. A new LMI based stability test for the existence of switched Lyapunov functions is first developed. If a switched Lyapunov function exists, asymptotic stability of the switched system also implies its exponential stability. An LMI optimization problem is then formulated to find a bound on the decay rate of the system. To attain the bound, state feedback control gains are designed. Using the same framework and the well-known S-procedure, a generalized sufficient LMI condition is obtained which guarantees a γ-performance of the closed-loop switched systems subject to input disturbances.