Stabilisation for 2-D discrete-time switched nonlinear systems with mixed time-varying delays under all modes unstable

Abstract

The problem of delay-dependent stability is concerned for two-dimensional switched systems in Fornasini-Marchesini local state-space model with mixed time-varying delays and with a class of generalised Lipschitz nonlinearities in this paper. The mixed time-varying delays consist of both the discrete and the distributed delays, and the time-varying delays are allowed in the states. Adopting the fast average dwell-time switching technique with Lyapunov functional, a sufficient condition of the exponential stability for two-dimensional nonlinear switched systems with all subsystems unstable is derived in terms of linear matrix inequality. Specifically, two-dimensional Abel lemma-based finite-sum inequalities approach and Jensen inequalities approach are applied to reduce the conservativeness of the result. The obtained result on stability analysis is then utilised to design a dynamic output feedback controller to stabilise the nonlinear closed-loop switched system. Finally, two numerical examples are shown to demonstrate the validity of the proposed results.

Keywords:

• All subsystems unstable
• two-dimensional(2-D)
• nonlinear switched systems
• mixed time-delays
• dynamic output feedback (DOF)
• exponential stability

Disclosure statement

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

Additional information

Funding

This work was partially supported by the S&T Program of Hebei under Grant (F2020203037), National Key Research and Development Program of China under Grant (2018YFB1308300), National Natural Science Foundation of China (61933009, 61751309, 618255304), Natural Science Foundation of Hebei under Grant (F2020203013).

Notes on contributors

Dan Peng

Dan Peng received her B.S. degree in applied mathematics from Beihua University, Jilin, China in 2001, and an M.S. degree in Operational Research and Cybernetics and a Ph.D. degree in Control Theory and Control Engineering, both from Yanshan University in 2003, and 2008. From 29 March 2018 to 29 March 2019, she did research as an academic visitor at Bournemouth University, UK, funded by China Scholarship Council. Now she is a Professor of the School of Science, Yanshan University, Qinhuangdao, China. Her research interests include time-delay systems, nonlinear systems and 2-D systems.

Hanmei Nie

Hanmei Nie received her B.S. degree in Mathematics and Applied Mathematics from Hebei university of science and technology, Shijiazhuang,China, in 2017. And she received her M.S. degree in School of Science, Yanshan university, Qinhuangdao, China, in 2020. Her research interests include time-delay systems and 2-D systems.