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Regional stability of positive switched linear systems with multi-equilibrium points

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Abstract

This paper studies the regional stability for positive switched linear systems with multi-equilibrium points (PSLS-MEP). First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common linear Lyapunov function. Second, by establishing multiple Lyapunov functions, a dwell time based condition is proposed for the regional stability analysis. Third, a suprasphere which contains all equilibrium points is constructed as a stability region of the considered PSLS-MEP, which is less conservative than existing results. Finally, the study of an illustrative example shows that the obtained results are effective in the regional stability analysis of PSLS-MEP.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Zhi Liu & Yu-Zhen Wang

Authors
  1. Zhi Liu
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  2. Yu-Zhen Wang
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Corresponding author

Correspondence to Zhi Liu.

Additional information

This work was supported by the NNSF of China (No. 61374065), and the Research Fund for the Taishan Scholar Project of Shandong Province.

Recommended by Associate Editor Qing-Long Han

Zhi Liu received the B. Sc. degree from School of Mathematics and Information, Ludong University, China in 2009, and the M. Sc. degree from School of Mathematical Science, University of Jinan, China in 2013. Since 2013 she is a Ph.D. degree candidate at School of Control Science and Engineering, Shandong University, China.

Her research interests include positive systems and switched systems.

ORCID iD: 0000-0002-4745-9025

Yu-Zhen Wang graduated from Taian Teachers College, China in 1986, received the M. Sc. degree from Shandong University of Science and Technology, China in 1995, and the Ph.D. degree from Institute of Systems Science, Chinese Academy of Sciences, China in 2001. Since 2003, he is a professor with School of Control Science and Engineering, Shandong University, China, and now the dean of the School of Control Science and Engineering, Shandong University. From 2001 to 2003, he worked as a postdoctoral fellow in Tsinghua University, China. From March 2004 to June 2004, from Februery 2006 to May 2006 and from November 2008 to January 2009, he visited City University of Hong Kong as a research fellow. From September 2004 to May 2005, he worked as a visiting research fellow at the National University of Singapore. He received the Prize of Guan Zhaozhi in 2002, the Prize of Huawei from the Chinese Academy of Sciences in 2001, the Prize of Natural Science from Chinese Education Ministry in 2005, and the National Prize of Natural Science of China in 2008. Currently, he is an associate editor IMA Journal of Mathematical Control and Information, and a Technical Committee member of IFAC.

His research interests include nonlinear control systems, Hamiltonian systems and Boolean networks.

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Liu, Z., Wang, YZ. Regional stability of positive switched linear systems with multi-equilibrium points. Int. J. Autom. Comput. 14, 213–220 (2017). https://doi.org/10.1007/s11633-016-1003-5

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  • DOI: https://doi.org/10.1007/s11633-016-1003-5

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