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New Explicit Criteria for Finite-time Stability of Singular Linear Systems Using Time-dependent Lyapunov Functions

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  • Control Theory and Applications
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Abstract

In this paper, the finite time stability and H∞ finite-time stability of singular linear systems are considered. By constructing a class of time-dependent Lyapunov functions and introducing a zero term with free weighting matrices, we first establish a new explicit criterion in the form of LMIs for finite-time stability of the system. Then, an H∞ finite-time stability criterion for the system is obtained. The given results are easily verifiable and less conservative compared with some existing ones in the literature. Finally, four numerical examples are given to demonstrate the effectiveness of the proposed method.

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Funding

The authors thank the reviewers for their valuable comments on this paper. This work is supported by the National Natural Science Foundation of China under Grant 61873110 and Taishan Scholar Foundation of Shandong Province under Grant ts20190938.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, Jinan, Shandong Province, 250022, China

    Qian Ma & Yuangong Sun

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  1. Qian Ma
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  2. Yuangong Sun
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Correspondence to Yuangong Sun.

Additional information

Qian Ma received her B.S. degree in mathematics and applied mathematics from the Dongchang College of Liaocheng University, China, in 2018. Now, she is a graduate student at School of Mathematical Sciences, University of Jinan. Her research interests include singular systems and delay systems.

Yuangong Sun received his Ph.D. degree in general mechanics and foundation of mechanics from Peking University, Beijing, China. He is now a professor in School of Mathematical Sciences, University of Jinan, China. He has over 90 publications in journals and conference proceedings on topics concerning stability and control of switched systems, and cooperative control of multi-agent systems. In addition, he has served as the Principle Investigator of more than 5 projects sponsored by Natural Science Foundations of China. His research focuses on switched systems and multi-agent systems.

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Ma, Q., Sun, Y. New Explicit Criteria for Finite-time Stability of Singular Linear Systems Using Time-dependent Lyapunov Functions. Int. J. Control Autom. Syst. 20, 1186–1193 (2022). https://doi.org/10.1007/s12555-020-0873-z

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  • DOI: https://doi.org/10.1007/s12555-020-0873-z

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