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Stability criterion of linear delayed impulsive differential systems with impulse time windows

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Abstract

In this paper, we study the uniform stability of linear delayed differential equationswith impulse time windows. By means of Lyapunov functions and Razumikhin technique combined with classification discussion technique, the criterion of uniform stability is obtained, which may be used to discuss others stability of delayed differential equations with impulse time win-dows. Two examples are given to illustrate the effectiveness of the theoretic result.

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Author information

Authors and Affiliations

  1. College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, PR China

    Huamin Wang, Shukai Duan, Chuandong Li & Lidan Wang

  2. Department of Mathematics, Luoyang Normal University, Luoyang, Henan, 471022, PR China

    Huamin Wang

  3. Department of Electrical and Computer Engineering Texas A&M University at Qatar., PO Box 23874, Doha, Qatar

    Tingwen Huang

Authors
  1. Huamin Wang
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  2. Shukai Duan
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  3. Chuandong Li
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  4. Lidan Wang
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  5. Tingwen Huang
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Corresponding author

Correspondence to Shukai Duan.

Additional information

Recommended by Associate Editor Izumi Masubuchi under the direction of Editor Fuchun Sun. This work was supported by Program for New Century Excellent Talents in University (Grant Nos.[2013]47), National Natural Science Foundation of China (Grant Nos. 61372139, 61374078, 61503175, 61571372), Fundamental Research Funds for the Central Universities (Grant Nos. XDJK2014A009), High School Key Scientific Research Project of Henan Province (Grant No.15A120013). This publication was made possible by NPRP grant 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 author[s].

Huamin Wang received his B.S. degree in Applied Mathematics from Chongqing University, Chongqing, China in 2003, and M.S. degree in Applied Mathematics from Henan Normal University, Xinxiang, China in 2012. He is currently pursuing a Ph.D. degree with College of Electronic and Information Engineering, Southwest university, Chongqing, China. His current research interest covers compu-tational intelligence, neural networks, stability analysis of impulsive dynamical systems.

Shukai Duan received his Ph.D. in Computer Science from Chongqing University, China, in 2006. Dr. Duan has been with the College of Electronics and Information Engineering, Southwest University, Chongqing, China, since 1996, serving as professor from 2010. He also serves as an IEEE member and an IEEE CIS member. He was a visiting professor at University of Michigan in 2010, University of Windsor in 2013, and Texas A&M University at Qatar in 2014, respectively. His research interests include memristor devices and memristive system, nonlinear circuits and systems, artificial neural networks, chaos and chaotic circuit, intelligent signal processing. He has published four books and more than 100 papers in refereed journals and conferences.

Chuandong Li received his B.S. degree in Applied Mathematics from Sichuan University, Chengdu, China in 1992, and M.S. degree in operational research and control theory and Ph.D. degree in Computer Software and Theory from Chongqing University, Chongqing, China, in 2001 and in 2005, respectively. He has been a Professor at the College of Computer Science, Chongqing University, Chongqing 400044, China, since 2007, and been the IEEE Senior member since 2010. From November 2006 to November 2008, he serves as a research fellow in the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong, China. He has published about more than 100 journal papers. His current research interest covers computational intelligence, neural networks, memristive systems, chaos control and synchronization, and impulsive dynamical systems.

Lidan Wang received her B.E. degree in automatic control from Nanjing University of Science and Technology, China, in 1999 and the Ph.D. degree in Computer Software and Theory from the Chongqing University, China, in 2008. Currently, she is a professor in the School of Electronics and Information Engineering, Southwest University, Chongqing, China. Her research interests include the nonlinear system and chaotic circuit, artificial neural networks and FPGA technology, Memristor and Memristive systems. She has published more than 20 academic papers in the fields of chaos in electronic circuits and chaotic communications.

Tingwen Huang received his B.S. degree from Southwest Normal University (now Southwest University), China, in 1990, his M.S. degree from Sichuan University, China, in 1993, and his Ph.D. degree from Texas A&M University, College Station, Texas, USA, in 2002. He is a Professor of Mathematics, Texas A&M University at Qatar. His current research interests include dynamical systems, memristor, neural networks, complex networks, optimization and control, traveling wave phenomena.

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Wang, H., Duan, S., Li, C. et al. Stability criterion of linear delayed impulsive differential systems with impulse time windows. Int. J. Control Autom. Syst. 14, 174–180 (2016). https://doi.org/10.1007/s12555-014-0236-8

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  • DOI: https://doi.org/10.1007/s12555-014-0236-8

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