Input and output strictly passive H_∞ control of discrete-time switched systems

Abstract

This paper is concerned with the problem of $H_\infty $H∞ control based on input and output strict passivity for discrete-time switched systems in both linear and nonlinear texts. Firstly, a sufficient condition is derived by using multiple storage functions, Lie derivative and iteration technique, which can guarantee that the discrete-time switched nonlinear system is asymptotically stable and satisfies a prescribed $H_\infty $H∞ performance index. Secondly, the above result is extended to the discrete-time switched linear system based on the linear matrix inequality approach, and each sub-controller with an explicit expression is given. Finally, two numerical examples are given to illustrate the effectiveness and the applicability of the proposed method.