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Region stability analysis for switched nonlinear systems with multiple equilibria

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  • Control Theory and Applications
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Abstract

This paper investigates the region stability analysis for switched nonlinear systems whose subsystems have different equilibria, which are referred to multi-equilibrium switched nonlinear systems, and proposes a number of new results on the region stability analysis. Through investigating the dynamical behavior of the multi-equilibrium switched system, two methods are established, based on which several new results are then obtained for the region stability. It is shown that the main results obtained in this paper not only guarantee the region stability of the multi-equilibrium switched nonlinear system under arbitrary switching, but also provide several new approaches to determine the corresponding regions of convergence. Moreover, an improved average dwell time (ADT) method is proposed for the stability of switched nonlinear systems whose subsystems do not share a common Lyapunov function. Finally, an illustrative example with numerical simulation is studied by using the obtained results. The study of example shows that our results work very well in analyzing the region stability of some multi-equilibrium switched nonlinear systems.

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Authors and Affiliations

  1. School of Science, Qilu University of Technology, Jinan, 250353, P. R. China

    Rong-Wei Guo

  2. School of Control Science and Engineering, Shandong University, Jinan, 250061, P. R. China

    Yu-Zhen Wang

Authors
  1. Rong-Wei Guo
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  2. Yu-Zhen Wang
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Corresponding author

Correspondence to Rong-Wei Guo.

Additional information

Recommended by Associate Editor Yingmin Jia under the direction of Editor Duk-Sun Shim. This work is supported by National Natural Science Foundation of China [61573218, 61403236, 61304133, 61473173].

Rongwei Guo was born in Jinan, China in 1979. He received his B.S. degree in Mathematics from University of Jinan, Jinan, China, in 2001, and his M.S. and Ph.D. degrees in Mathematics of Shanghai University and Shandong University, China, in 2004 and 2011, respectively. He joined School of Science at Qilu University of Technology in 2004, where he is currently a professor. His research interests include nonlinear systems, switched systems.

Yuzhen Wang was born in Tai’an, China in 1963. He graduated from Tai’an Teachers College in 1986,received his MS degree from Shandong University of Science& Technology in 1995 and his PhD degree from the Institute of Systems Science, Chinese Academy of Sciences in 2001. From 2001 to 2003, he worked as a Postdoctoral Fellow in Tsinghua University, Beijing,China. Since 2003, he is a professor with the School of Control Science and Engineering, Shandong University, China, and the director of the 13 Institute of Automatic Control, Shandong University. From Mar. 2004 to Jun. 2004, from Feb. 2006 to May 2006 and from Nov 2008 to Jan 2009, he visited City University of Hong Kong as a Research Fellow. From Sept. 2004 to May 2005, he worked as a visit Research Fellow at the National University of Singapore. His research interests include nonlinear control 19 systems, Hamiltonian systems and robust control.Dr Wang 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 of Asian Journal of Control, and IMA Journal of Math Control and Inform.

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Guo, RW., Wang, YZ. Region stability analysis for switched nonlinear systems with multiple equilibria. Int. J. Control Autom. Syst. 15, 567–574 (2017). https://doi.org/10.1007/s12555-016-0006-x

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