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New Stability Conditions of Linear Switched Singular Systems by Using Multiple Discontinuous Lyapunov Function Approach

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Abstract

In this paper, the problem of the E-exponential stability of linear switched singular systems composed of stable and unstable subsystems in discrete-time case is investigated. By using a multiple discontinuous Lyapunov function approach and exploring the properties of mode-dependent average dwell time(MDADT) switching signal, new sufficient conditions of E-exponential stability for linear switched singular systems are presented. Compared with the existing results, the proposed method is more flexible and tighter bounds on MDADT can be obtained. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan, 450001, China

    Jumei Wei, Huimin Zhi & Xiaowu Mu

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  1. Jumei Wei
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  2. Huimin Zhi
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  3. Xiaowu Mu
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Correspondence to Jumei Wei.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Young Ik Son under the direction of Editor PooGyeong Park. This work was supported by The National Natural Science Foundation of China (grant nos. 11401540, 11571322) and the Foundation of Henan Educational Committee, China (grant No.17A110031). The authors would like to thank the Editor, the Associate Editor, and anonymous reviewers for their constructive comments.

Jumei Wei received her B.S., M.S. and Ph.D. degrees from the School of Mathematics and Statistics of Zhengzhou University. Currently, she is an Associate Professor in Zhengzhou University. Her research interests include hybrid systems, singular systems and networked control systems.

Huimin Zhi received her bachelor degree from Anyang Normal university in 2016. Currently, she is a master student in the School of Mathematics and Statistics of Zhengzhou University. Her research interests include singular systems, network control systems, and switched systems.

Xiaowu Mu received his B.S., M.S. and Ph.D. degrees from the Department of Mathematics of Peking University, in 1983, 1988, and 1991, respectively. Currently, he is a Professor in Zhengzhou University. His research interests include hybrid systems and networked control systems.

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Wei, J., Zhi, H. & Mu, X. New Stability Conditions of Linear Switched Singular Systems by Using Multiple Discontinuous Lyapunov Function Approach. Int. J. Control Autom. Syst. 17, 3122–3130 (2019). https://doi.org/10.1007/s12555-018-0480-4

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