Global output feedback control for a class of high-order switched nonlinear systems with time-varying delays

Abstract

This paper focuses on the output feedback stabilisation problem for a class of high-order switched nonlinear systems with time-varying delays. The powers and the nonlinear terms are dependent on the switching signal. Firstly, a homogeneous output-feedback controller is designed for the nominal switched system by virtue of adding a power integrator technique. Then, with the help of the homogeneous domination approach, homogeneous output feedback controllers are designed with series scaling gains. By successfully constructing an appropriate Lyapunov–Krasovskii functional for the stability analysis, it is shown that the resulted closed-loop system is globally asymptotically stable. In addition, the proposed control scheme can be extended to a class of high-order switched upper-triangular nonlinear systems with time-varying delays. Two examples are given to illustrate the effectiveness of the proposed method.

Keywords:

• Output feedback
• switched nonlinear system
• time-varying delays
• Lyapunov–Krasovskii functional
• homogeneous domination

Disclosure statement

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

ORCID

Yan Jiang http://orcid.org/0000-0001-6031-8457

Junyong Zhai http://orcid.org/0000-0001-5122-3819

Additional information

Funding

This work is supported in part by the National Natural Science Foundation of China [grant number 61873061], Qing Lan Project, and PAPD.

Notes on contributors

Yan Jiang

Yan Jiang received her PhD degree in Automatic Control from Southeast University, Nanjing, China, in 2020, and her MS degree from Guangxi University, Nanning, China, in 2016. She is an assistant professor at School of Electrical Engineering, Guangxi University. Her research interests include switched systems, nonlinear systems, time-delay systems, adaptive control and sampled-data control.

Junyong Zhai

Junyong Zhai received his PhD degree in Automatic Control from Southeast University in 2006. From September 2009 to September 2010, he was a postdoctoral research fellow at the University of Texas at San Antonio. He is a professor at the School of Automation, Southeast University. His research interests include nonlinear systems control, robot control, stochastic time-delay systems, and multiple models switching control.