Non-fragile H_∞ control of periodic piecewise time-varying systems based on matrix polynomial approach

Abstract

This paper investigates the problem of non-fragile $H_{\mathrm{\infty }}$ control for periodic piecewise time-varying systems. Based on a Lyapunov function with continuous time-varying Lyapunov matrix polynomial, and combining with the positiveness and negativeness properties of matrix polynomials, the $H_{\mathrm{\infty }}$ performance analysis is first accomplished. Then consider two types of controller gain perturbations that are formulated by time-varying matrix parameters and norm-bounded uncertainties. The additive and multiplicative non-fragile controllers to guarantee the $H_{\mathrm{\infty }}$ performance of the system are formed, of which the controller gain could be solved with linear matrix inequalities directly. The designed non-fragile $H_{\mathrm{\infty }}$ controller is desirable in applications. Finally, numerical examples demonstrate the effectiveness of the proposed methods.

Keywords:

• Periodic piecewise systems
• non-fragile control
• Lyapunov matrix polynomials

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes on contributors

Yun Liu received the M.S. degree in control science and engineering from Guangdong University of Technology, Guangzhou, China, in 2020. He is currently pursuing the Ph.D degree in control science and engineering with the East China University of Science and Technology, Shanghai, China. His current research interests include periodic systems, switched systems, network security, and distributed filtering.

Panshuo Li received the B.S. degree in mechanical engineering from Donghua University, Shanghai, China, the M.S. degree from Shanghai Jiao Tong University, Shanghai, China, in 2009 and 2012, and the Ph.D. degree in mechanical engineering from The University of Hong Kong, Hong Kong, in 2016. Since 2016, she has been an Associate Professor with the School of Automation, Guangdong University of Technology, Guangzhou, China. Her current research interests include switched systems, periodic systems, intelligent vehicle control, and vibration control.

Bin Zhang received the Ph.D. degree in control science and engineering from Central South University, Changsha, China, in 2016. Since 2017, she has been with the Guangdong University of Technology, Guangzhou, China, where she is currently a Lecturer with the School of Automation. Her current research interests include complex process modeling and optimization, intelligent algorithms, and their applications.

Additional information

Funding

The work was supported in part by the National Natural Science Foundation of China [grant number 62073083], in part by the Local Innovative and Research Teams Project of Guangdong Special Support Program [grant number 2019BT02X353], and in part by the Guangdong Natural Science Funds for Distinguished Young Scholar [grant number 2019B151502026].