Non-fragile stabilisation of nonlinear switched systems with actuator saturation

Abstract

For nonlinear continuous-time switched systems, the problem of how to overcome the controller vulnerability is studied when the saturating actuator is considered. The sufficient condition of non-fragile stabilisation of the system is derived by using the method of multiple Lyapunov functions. Then, a switching law and the non-fragile state feedback controllers are designed such that the closed-loop system can be asymptotically stabilised at the origin. Finally, when some scalar parameters of the closed-loop system are given, the design issue of the non-fragile state feedback controllers and the switching law, which aim at enlarging the estimation of domain of attraction for closed-loop system, is transformed into a convex optimisation issue with linear matrix inequalities (LMI) constraints, and a numerical example is given to verify the effectiveness of the proposed method.

KEYWORDS:

• Actuator saturation
• nonlinear switched systems
• non-fragile
• multiple Lyapunov functions
• LMI

Disclosure statement

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

Additional information

Funding

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

Notes on contributors

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.

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.