Asynchronous Stabilization of Discrete-Time Switched Linear Systems Under Dwell-Time Constraints

This article investigates the asynchronous stabilization problem for a class of discrete-time switched linear systems under dwell-time constraints. A novel conception called “basic pattern” is proposed which can precisely characterize all the admissible sequences of switched systems under asynchronous switching. Compared to existing methods which are devoted to constructing different Lyapunov functions for achieving less conservative stability conditions, here we report a convex stability criteria of asynchronously switched linear systems based on the established basic patterns. The derived stability conditions depend on an integer parameter that can be possibly unbounded to reach the nonconservativeness. The convex feature of the proposed stability criterion further facilitates the computation of the $l_{2}$-gain and $H_{\infty }$ control problems. Simulation results verify the validity of the derived theories and demonstrate that the proposed controller outperforms several controllers reported in previous literature.