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Stability of nonlinear systems with variable-time impulses: B-equivalence method

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  • Control Theory and Applications
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Abstract

This paper addresses the stability problem of nonlinear systems with variable-time impulses. By B-equivalence method, we shall show that under the well-selected conditions each solution of the considered systems will intersect each surface of discontinuity exactly once, and that the considered systems can be reduced to the fixed-time impulsive ones, which can be regarded as the comparison systems of the considered variable-time impulsive systems. Based on the stability theory of fixed-time impulsive systems, we propose a set of stability criteria for the variable-time impulsive systems. The theoretical results are illustrated by impulsive stabilization of Chua circuit.

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Author information

Authors and Affiliations

  1. Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, P. R. China

    Chuandong Li & Yinghua Zhou

  2. College of Mathematics Science, Chongqing Normal University, Chongqing, 401331, P. R. China

    Hui Wang

  3. School of Texas A&M University at Qatar, Doha, 23874, Qatar

    Tingwen Huang

Authors
  1. Chuandong Li
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  2. Yinghua Zhou
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  3. Hui Wang
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  4. Tingwen Huang
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Corresponding author

Correspondence to Chuandong Li.

Additional information

Recommended by Associate Editor Ho Jae Lee under the direction of Editor Yoshito Ohta. This work is supported by Natural Science Foundation of China (Grant nos: 61403313, 61374078) and the work was partially supported by Research Foundation of Key laboratory of Machine Perception and Children’s Intelligence Development funded by CQUE, China. This publication was made possible by NPRP Grant No. NPRP 4-1162-1-181 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.

Chuandong Li received his B.S. degree in Applied Mathematics from Sichuan University, Chengdu, China in 1992, and an M.S. degree in operational research and control theory and a Ph.D. degree in Computer Software and Theory from Chongqing University, Chongqing, China, in 2001 and 2005, respectively. He has been a professor at the College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China, since 2012, and been the IEEE Senior member since 2010. From November 2006 to November 2008, he served as a research fellow in the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong, China. He has published more than 100 journal papers. His current research interest covers computational intelligence, neural networks, memristive systems, chaos control and synchronization, and impulsive dynamical systems.

Yinghua Zhou received his B.S. degree in Communication Engineering from Chongqing University of Posts and Telecommunications, Chongqing, China in 2003, and his M.S. degree in Communication and information system from Chongqing University of Posts and Telecommunications, Chongqing, China, in 2006. He is currently pursuing a Ph.D. degree with College of Electronic and Information Engineering, Southwest University, Chongqing, China. His current research interests include neural networks, memristive systems, stability and synchronization of impulsive dynamics systems.

Hui Wang received her B.S. degree in Applied Mathematics from Chongqing Normal University, Chongqing, China in 1999, and an M.S. degree in operational research and control theory and a Ph.D. degree in Computer Software and Theory from Chongqing University, Chongqing, China, in 2003 and in 2007, respectively. He has been a professor at the College of Mathematics Theory, Chongqing Normal, Chongqing 400044, China, since 2014. She has published more than 30 journal papers. Her current research interest covers computational intelligence, memristive systems, chaos control and synchronization, and impulsive dynamical systems.

Tingwen Huang obtained his B.S. from Southwest Normal University in 1990, an M.S. from Sichuan University in 1993 and a Ph.D. from Texas A&M University in 2002. After he graduated at Texas A&M University, he has been working in Mathematics Department of Texas A&M University as Visiting Assistant Professor. In 2003, he started to work at Texas A&M University at Qatar until now. He now is an associate professor of Mathematics. His research fields include neural networks, chaos and its applications, etc. He has published about 30 journal papers on neural networks and nonlinear dynamics.

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Li, C., Zhou, Y., Wang, H. et al. Stability of nonlinear systems with variable-time impulses: B-equivalence method. Int. J. Control Autom. Syst. 15, 2072–2079 (2017). https://doi.org/10.1007/s12555-016-0086-7

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  • DOI: https://doi.org/10.1007/s12555-016-0086-7

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