Stability criteria of switched systems with a binary -dependent average dwell time approach

Abstract

This paper proposes a new concept of binary -dependent average dwell time, which describes different types of switching signals by the different grouping function $\mathcal{B}ϝ$ for switched systems. Then, combing with the improved multiple Lyapunov function approach, the issues of stability and stabilisation for switched linear systems under the proposed strategy are investigated for the first time, which unify the classical average dwell time (ADT), mode dependent ADT, edge dependent ADT, and Φ dependent ADT, and are more flexible and practical than other existing criteria. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.

Keywords:

• Switched systems
• stability
• stable subsystem
• binary -dependent average dwell time

Disclosure statement

The authors declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work.

Additional information

Funding

This work is supported by Fundamental Research Program of Shanxi Province [grant number 202103021224249] and Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province [grant number 20220023].

Notes on contributors

Qiang Yu

Qiang Yu was born in Handan, Hebei, China. He received his BS degree in Mathematics Education from Shi He Zi University, China, in 2003, and obtained his M.S. in Applied Mathematics and Ph.D. in Basic Mathematics from Shaanxi Normal University, China, in 2009 and 2014, respectively. From 2009 to 2011, he was with Heng Shui University as an instructor. In Jul. 2014, he joined Shanxi Normal University, China, where he is an Associate Professor at the School of Mathematics and Computer Science. From Aug. 2019 to Aug. 2020, he had been a visiting professor at Shibaura Institute of Technology, Japan. His research interests are stability of switching systems, positive systems, robust control and time-delay systems, etc.

Na Wei

Na Wei received the B.S. degree in mathematics and applied mathematics from Changzhi University, Changzhi, China, in 2020. She is currently pursuing the masters degree in system and control theory with Shanxi Normal University, Taiyuan, China. Her current research interests include fractional order systems and positive switched systems.