Stability analysis and asynchronous control of discrete-time cyclic switched systems with unstable subsystems

This paper studies the stability analysis and asynchronous control problems of discrete-time cyclic switched systems consisting of both stable and unstable subsystems based on slow/fast cycle-dependent average dwell time (ADT) switching. By Kronecker delta function, the cycle-dependent convex Lyapunov function (CLF) is first devised for the cyclic switched systems. It should be pointed out that the Lyapunov function has remarkably less conservativeness and more flexibility compared to traditional multiple Lyapunov function (MLF). Asynchronous cycle-dependent CLF and time-varying controller are proposed to investigate the asynchronous switching control of cyclic switched systems, and the relationship between the synchronous running time of stabilizable and unstabilizable subsystems and asynchronous time is characterized in the cycle. Finally, a numerical example and an application example are provided to illustrate the effectiveness of the proposed method.