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Exponential Stability of Neural Networks with Markovian Switching Parameters and General Noise

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  • Control Theory and Applications
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Abstract

This paper investigates the problem of exponential stability of Neural Networks (NNs) with Markovian parameters and general noise. The model in this paper with general noise is more suitable for many real nervous systems than NNs with white noise. Criteria for the exponential stability of the NNs with Markovian switching parameters and general noise in both the mean square and p-th moment are derived by utilizing the random analysis method and Lyapunov functional method techniques. The exponential stability of NNs without Markovian switching is given as a special case. Finally, simulation result in two examples are discussed to illustrate the theoretical results.

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Authors and Affiliations

  1. School of Information Science and Technology, Donghua University, No. 2999, Renmin North Road, Songjiang District, Shanghai, 201620, China

    Xin Zhang, Wuneng Zhou & Yuqing Sun

Authors
  1. Xin Zhang
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  2. Wuneng Zhou
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  3. Yuqing Sun
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Corresponding author

Correspondence to Wuneng Zhou.

Additional information

Recommended by Associate Editor Sing Kiong Nguang under the direction of Editor Hamid Reza Karimi. This work was partially supported by the Natural Science Foundation of China (grant no. 61573095), the Natural Science Foundation of Shanghai (Grant No. 15ZR1401800).

Xin Zhang received the B.S. and M.S. degrees in mathematics from Liaocheng University, Liaocheng, China, in 2012 and 2015, respectively. She is currently pursuing the Ph.D. degree in control science and engineering from Donghua University, Shanghai, China. Her current research interests include stability and control for neural networks, stochastic control with semi-Markov parameters.

Wuneng Zhou received the B.S. degree in mathematics from Huazhong Normal University, Hubei, China, in 1982, and the Ph.D degree in control science and engineering from Zhejiang University, Zhejiang, China, in 2005. He is currently a Professor with Donghua University, Shanghai, China. His current research interests include the stability, the synchronization and control for neural networks, wireless sensor networks, and complex networks.

Yuqing Sun received the B.S. degrees and she is currently pursuing the Ph.D. degree in control science and engineering from Donghua University, Shanghai, China, in 2014. Her current research interests include stochastic control with Levy process, control of neutral-type neural networks, and their applications on stochastic differential games and portfolio strategy.

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Zhang, X., Zhou, W. & Sun, Y. Exponential Stability of Neural Networks with Markovian Switching Parameters and General Noise. Int. J. Control Autom. Syst. 17, 966–975 (2019). https://doi.org/10.1007/s12555-018-0202-y

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  • DOI: https://doi.org/10.1007/s12555-018-0202-y

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