TY - JOUR
T1 - New Stability Conditions for Switched Linear Systems
T2 - A Reverse-Timer-Dependent Multiple Discontinuous Lyapunov Function Approach
AU - Li, Yang
AU - Xiang, Weiming
AU - Zhang, Hongbin
AU - Xia, Jianwei
AU - Zheng, Qunxian
N1 - Funding Information:
Manuscript received December 15, 2019; accepted December 26, 2019. Date of publication January 14, 2020; date of current version September 16, 2021. This work was supported in part by the National Natural Science Foundation of China under Grant 61971100, Grant 61603312, and Grant 61803001, and in part by the Natural Science Foundation of Anhui Province under Grant 1808085QF194. This article was recommended by Associate Editor H. R. Karimi. (Corresponding author: Hongbin Zhang.) Yang Li and Hongbin Zhang are with the School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China (e-mail: 13648065067@163.com; zhanghb@uestc.edu.cn).
Publisher Copyright:
© 2013 IEEE.
PY - 2021/10
Y1 - 2021/10
N2 - In this article, the stability issues are addressed for switched linear systems (SLSs) with mode-dependent average dwell time (MDADT). By dividing the dwell time into several segments, and constructing a reverse timer which starts timing at the end of each segment, we propose a new reverse-timer-dependent multiple discontinuous Lyapunov function (RTDMDLF), which is more general than the multiple Lyapunov function (MLF) and the multiple discontinuous Lyapunov function (MDLF). With the help of the RTDMDLF approach, several convex and nonconvex stability conditions are derived for SLSs with both stable and unstable subsystems, and the relation of these conditions and existing ones is revealed. Moreover, the stability conditions for SLSs with all stable subsystems are also given. All the results are presented in terms of infinite-dimensional linear matrix inequalities (LMIs), which can be relaxed into computable conditions by using a discretized approach. It is shown that the tighter bound of MDADT can be achieved by the RTDMDLF approach compared with those of the literature. Finally, the advantages of the results are illustrated within three numerical examples.
AB - In this article, the stability issues are addressed for switched linear systems (SLSs) with mode-dependent average dwell time (MDADT). By dividing the dwell time into several segments, and constructing a reverse timer which starts timing at the end of each segment, we propose a new reverse-timer-dependent multiple discontinuous Lyapunov function (RTDMDLF), which is more general than the multiple Lyapunov function (MLF) and the multiple discontinuous Lyapunov function (MDLF). With the help of the RTDMDLF approach, several convex and nonconvex stability conditions are derived for SLSs with both stable and unstable subsystems, and the relation of these conditions and existing ones is revealed. Moreover, the stability conditions for SLSs with all stable subsystems are also given. All the results are presented in terms of infinite-dimensional linear matrix inequalities (LMIs), which can be relaxed into computable conditions by using a discretized approach. It is shown that the tighter bound of MDADT can be achieved by the RTDMDLF approach compared with those of the literature. Finally, the advantages of the results are illustrated within three numerical examples.
KW - Mode-dependent average dwell time (MDADT)
KW - reverse-timer-dependent multiple discontinuous Lyapunov function (RTDMDLF)
KW - stability analysis
KW - switched linear systems (SLSs)
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U2 - 10.1109/TSMC.2019.2963142
DO - 10.1109/TSMC.2019.2963142
M3 - Article
AN - SCOPUS:85115216803
SN - 2168-2216
VL - 51
SP - 6564
EP - 6575
JO - IEEE Transactions on Systems, Man, and Cybernetics: Systems
JF - IEEE Transactions on Systems, Man, and Cybernetics: Systems
IS - 10
ER -