Quasi-time-dependent asynchronous H_∞ control of discrete-time switched systems with mode-dependent persistent dwell-time

This paper mainly concerns the issues of stability and l₂-gain for a class of discrete-time switched systems with mode-dependent persistent dwell-time (MPDT) under asynchronous switching. The asynchronous switching implies that the switchings of controllers do not coincide with those among subsystems, more specifically, there exists a time lag between two switchings. Stability criterion and l₂-gain analysis results are developed to guarantee that the asynchronously switched system is globally uniformly asymptotically stable with a specified H_∞ performance index. A quasi-time-dependent (QTD) Lyapunov-like function is proposed, upon which a set of mode-dependent and QTD H_∞ controllers is designed. A numerical example is provided to show the validity and advantage of the developed results.