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

ABSTRACT

This paper is concerned with the problem of $H_{\mathrm{\infty }}$ 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 $H_{\mathrm{\infty }}$ 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.

Keywords:

• Discrete-time switched systems
• input and output strict passivity
• $H_{\mathrm{\infty }}$ control
• multiple storage functions

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (grant no. 61802150), Shandong Provincial Natural Science Foundation (grant no. ZR2019MF059), Shandong Province Higher Educational Science and Technology Program (grant no. J16LB10), Doctoral Foundation of Weifang University (grant no. 2014BS11), Natural Science Foundation of Jiangsu Province (grant no. BK20170196) and the China Postdoctoral Science Foundation Funded Project (grant no. 2018M642161).