H∞ control of continuous switched systems based on input and output strict passivity

• Published in: IET control theory & applications 2018-09, Vol.12 (14), p.1951-1955
• Main Authors: Gao, Zairui, Wang, Ziyun, Ji, Zhicheng, Liu, Yunlong
• Format: Article
• Language: English
• Subjects: appropriate switching rule; asymptotic stability; authors study; constructing nonlinear controllers; continuous switched systems; continuous time systems; control problem; control system synthesis; H∞ control; input; linear matrix inequalities; linear systems; Lyapunov methods; nonlinear control systems; output strict passivity; sufficient condition; switched linear systems; switched nonlinear systems; time‐varying systems
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2017.1446

In this study, the authors study the issue of H∞ control of continuous switched systems based on the input and output strict passivity. First of all, for switched non‐linear systems, by constructing non‐linear controllers and an appropriate switching rule, a sufficient condition is given to guarantee the existence of a solution to the H∞ control problem based on the multiple Lyapunov functions method. It only requires that each subsystem exhibits input and output strict passivity in the activation interval, and not in the whole time domain. Next, for switched linear systems, a sufficient condition is obtained to guarantee the existence of a solution to the H∞ control problem based on the linear matrix inequality, and the controllers with explicit expressions of subsystems are designed. Finally, two examples are given to verify the feasibility and effectiveness of the results.