New stability and stabilization results for discrete-time switched systems

In this paper, the stability and stabilization problems are considered for discrete‐time switched systems in both nonlinear and linear contexts. By introducing the concept of forward average dwell time and using multiple‐sample Lyapunov‐like functions variation, the extended stability results for discrete‐time switched systems in the nonlinear setting are first derived. Then, the criteria for stability and stabilization of linear switched systems are obtained via a newly constructed switching strategy, which allows us to obtain exponential stability results. A new kind of mode‐dependent controller is designed to realize the stability conditions expressed by the multiple‐sample Lyapunov‐like functions variation. Based on this controller, the stabilization conditions can be given in terms of linear matrix inequalities (LMIs), which are easy to be checked by using recently developed algorithms in solving LMIs. Finally, a numerical example is provided to show the validity and potential of the results.