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Delay-Dependent Robust Exponential Stability of Impulsive Markovian Jumping Reaction-Diffusion Cohen-Grossberg Neural Networks

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Abstract

This paper is devoted to investigating delay-dependent robust exponential stability for a class of Markovian jump impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks (IRDCGNNs) with mixed time delays and uncertainties. The jumping parameters, determined by a continuous-time, discrete-state Markov chain, are assumed to be norm bounded. The delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing a Lyapunov–Krasovskii functional, and using poincarè inequality and the mathematical induction method, several novel sufficient criteria ensuring the delay-dependent exponential stability of IRDCGNNs with Markovian jumping parameters are established. Our results include reaction-diffusion effects. Finally, a Numerical example is provided to show the efficiency of the proposed results.

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Acknowledgments

The author would like to thank the Editor and the referees for their detailed comments and valuable suggestions which considerably improved the presentation of the paper. This research is supported by the National Natural Science Foundations of China (60974025, 60939003), National 863 Plan Project (2008AA04Z401, 2009AA043404), the Natural Science Foundation of Shandong Province (No. Y 2007G30), Natural Science Foundation of Guangxi Autonomous Region (No. 2012GXNSFBA053003), the Scientific and Technological Project of Shandong Province (No. 2007GG3WZ04016), the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (HIT.NSRIF.2001120), the China Postdoctoral Science Foundation (2010048 1000) and the Shandong Provincial Key Laboratory of Industrial Control Technique (Qingdao University).

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Authors and Affiliations

  1. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, People’s Republic of China

    Yonggui Kao & Changhong Wang

  2. Shandong Provincial Key Laboratory of Industrial Control Technology, Qingdao University, Qingdao, 266071, China

    Yonggui Kao

  3. Division of Adult & Graduate Studies, Eastern Nazarene College, Quicy, MA, USA

    Lin Zhang

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  1. Yonggui Kao
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  2. Changhong Wang
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Correspondence to Yonggui Kao.

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Kao, Y., Wang, C. & Zhang, L. Delay-Dependent Robust Exponential Stability of Impulsive Markovian Jumping Reaction-Diffusion Cohen-Grossberg Neural Networks. Neural Process Lett 38, 321–346 (2013). https://doi.org/10.1007/s11063-012-9269-2

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