Guaranteed cost control and anti-windup design of saturated switched systems

Abstract

In this paper, the problem of guaranteed cost control and anti-windup design is studied for a class of switched systems with actuator saturation. The switching strategy and anti-windup compensator are designed to ensure the asymptotic stability of the closed-loop system and to obtain the minimum upper bound of the cost function. Some sufficient conditions for the existence of an anti-windup compensator of guaranteed cost are given by using the multiple Lyapunov functions method. On this basis, the minimum upper bound of the cost function is determined by solving the optimisation problem under the constraint of linear matrix inequality (LMI). Finally, a numerical example is given to verify the effectiveness of the proposed method.

Keywords:

• Guaranteed cost control
• switched systems with actuator saturation
• anti-windup
• multiple Lyapunov functions
• LMI

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Natural Science Foundation of Liaoning Province of China [grant numbers 2020-MS-283 and 20180551014] and the Scientific Research Fund of Education Department of Liaoning Province of China [grant number L2019016].

Notes on contributors

Xinquan Zhang

Xinquan Zhang received the B.Sc. degree in Automation and M.Sc. degree in Control Theory & Engineering from Liaoning Technical University in Fuxin, China, in 2003 and 2007, respectively. He completed his Ph.D. in Control Theory and Control Engineering in 2012 at the College of Information Science & Engineering, of the Northeastern University of Shenyang, China. Since 2017, as an associate professor, he has been with School of Information and Control Engineering, Liaoning Petrochemical University, China. His research interests include switched systems, robust control and systems control under constraints.

Jianlin Wang

Jianlin Wang received the B.S. degree from Yingkou Institute of Technology, Yingkou, China. Now he is working towards the Master degree at School of Information and Control Engineering, Liaoning Petrochemical University, Fushun, China. His research interest focuses on switched systems and non-fragile control.