Stability analysis for discrete-time switched systems with unstable subsystems by a mode-dependent average dwell time approach

Hongbin Zhang; Dehua Xie; Hongyu Zhang; Gang Wang

doi:10.1016/j.isatra.2014.05.020

Stability analysis for discrete-time switched systems with unstable subsystems by a mode-dependent average dwell time approach

ISA Trans. 2014 Jul;53(4):1081-6. doi: 10.1016/j.isatra.2014.05.020. Epub 2014 Jun 9.

Authors

Hongbin Zhang¹, Dehua Xie², Hongyu Zhang³, Gang Wang⁴

Affiliations

¹ School of Automation, Nanjing University of Science and Technology, Nanjing, Jiangsu 210049, China; School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China. Electronic address: zhanghb@uestc.edu.cn.
² School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China. Electronic address: xiedehua1005@163.com.
³ School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China. Electronic address: hyzhang@uestc.edu.cn.
⁴ School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China. Electronic address: wanggangisi@gmail.com.

PMID: 24925136
DOI: 10.1016/j.isatra.2014.05.020

Abstract

This paper mainly intends to present new stability results of a discrete-time switched system with unstable subsystems. By adopting multiple Lyapunov functions׳ (MLFs׳) method, new and less conservative stability conditions are derived in terms of a set of numerical feasible linear matrix inequalities (LMIs) with mode-dependent average dwell time (MDADT) techniques. Different from previous literatures, unstable subsystems are considered under two situations in this paper. It is shown that the discrete-time switched system can achieve exponential stability under a slow switching scheme and even in the presence of fast switching of unstable subsystems. Finally a numerical example is given to demonstrate the effectiveness of the proposed method.

Keywords: Mode-dependent average dwell time; Stability; Switched systems; Unstable subsystems.

Publication types

Research Support, Non-U.S. Gov't