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Comparison System Method for a class of Stochastic Systems with Variable-time Impulses

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  • Control Theory and Applications
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Abstract

This paper studies the stability of stochastic impulsive systems with variable-time impulses. We consider the case that the trajectory of the stochastic system intersects each surface of discontinuity exactly once. Then we shall show that under the well-selected conditions the variable-time impulsive systems can be reduced to the fixed-time impulsive systems with impulse time window. By using comparison method, we obtain two theorems to determine the different impulsive time windows for stable and unstable stochastic dynamical systems, respectively. The effectiveness of the theoretical results are illustrated by two numerical examples.

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Authors and Affiliations

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

    Jie Tan

  2. College of Mathematics and physics, Chongqing University of Science and Technology, Chongqing, 401331, China

    Jie Tan

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

    Chuandong Li

  4. Department of Electrical and Computer Engineering Texas A&M University at Qatar, Doha, Qatar

    Tingwen Huang

Authors
  1. Jie Tan
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  2. Chuandong Li
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  3. Tingwen Huang
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Corresponding author

Correspondence to Chuandong Li.

Additional information

Recommended by Editor Hamid Reza Karimi. This publication was supported by Natural Science Foundation of China (grant No.61374078,61633011) and the Science and Technology Foundation of the Education Department of Chongqing (KJ1501312, KJ1601310).

Jie Tan received her B.S. and M.S. degrees in Applied Mathematics from Southwest University, Chongqing, China, in 2002 and 2010, respectively. She is currently pursuing a Ph.D degree with College of Electronic and Information Engineering, Southwest University, Chongqing, China. Her current research interest covers computational intelligence, neural networks, stability analysis of impulsive dynamical systems.

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 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.

Tingwen Huang received his B.S. degree from Southwest Normal University (now Southwest University), China, in 1990, an M.S. degree from Sichuan University, China, in1993, and a 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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Tan, J., Li, C. & Huang, T. Comparison System Method for a class of Stochastic Systems with Variable-time Impulses. Int. J. Control Autom. Syst. 16, 702–708 (2018). https://doi.org/10.1007/s12555-017-0086-2

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  • DOI: https://doi.org/10.1007/s12555-017-0086-2

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