中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3325-3336.doi: 10.1088/1674-1056/18/8/037

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Robust stability analysis for Markovian jumping stochastic neural networks with mode-dependent time-varying interval delay and multiplicative noise

佟绍成1, 张化光2, 浮洁3, 马铁东3   

  1. (1)Department of Mathematics and Physics, Liaoning University of Technology, Jinzhou 121001, China; (2)Key Laboratory of Integrated Automation for the Process Industry, Ministry of Education, Northeastern University, Shenyang 110004, China;School of Information Science and Engineering, Northeastern University, Shenyang 110004, China; (3)School of Information Science and Engineering, Northeastern University, Shenyang 110004, China
  • 收稿日期:2008-11-23 修回日期:2009-02-13 出版日期:2009-08-20 发布日期:2009-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 60534010, 60774048, 60728307, 60804006, 60521003), the National High Technology Research and Development Program of China (863 Program) (Grant No 2006AA04Z183), the Natural Science Foundation of Liaoning Province of China (Grant No 20062018), 973 Project (Grant No 2009CB320601) and 111 Project (Grant No B08015).

Robust stability analysis for Markovian jumping stochastic neural networks with mode-dependent time-varying interval delay and multiplicative noise

Zhang Hua-Guang(张化光)a)b)†, Fu Jie(浮洁)b), Ma Tie-Dong(马铁东)b), and Tong Shao-Cheng(佟绍成)c)   

  1. a Key Laboratory of Integrated Automation for the Process Industry, Ministry of Education, Northeastern University, Shenyang 110004, China; b School of Information Science and Engineering, Northeastern University, Shenyang 110004, China; c Department of Mathematics and Physics, Liaoning University of Technology, Jinzhou 121001, China
  • Received:2008-11-23 Revised:2009-02-13 Online:2009-08-20 Published:2009-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 60534010, 60774048, 60728307, 60804006, 60521003), the National High Technology Research and Development Program of China (863 Program) (Grant No 2006AA04Z183), the Natural Science Foundation of Liaoning Province of China (Grant No 20062018), 973 Project (Grant No 2009CB320601) and 111 Project (Grant No B08015).

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摘要： This paper is concerned with the problem of robust stability for a class of Markovian jumping stochastic neural networks (MJSNNs) subject to mode-dependent time-varying interval delay and state-multiplicative noise. Based on the Lyapunov--Krasovskii functional and a stochastic analysis approach, some new delay-dependent sufficient conditions are obtained in the linear matrix inequality (LMI) format such that delayed MJSNNs are globally asymptotically stable in the mean-square sense for all admissible uncertainties. An important feature of the results is that the stability criteria are dependent on not only the lower bound and upper bound of delay for all modes but also the covariance matrix consisting of the correlation coefficient. Numerical examples are given to illustrate the effectiveness.

Abstract: This paper is concerned with the problem of robust stability for a class of Markovian jumping stochastic neural networks (MJSNNs) subject to mode-dependent time-varying interval delay and state-multiplicative noise. Based on the Lyapunov--Krasovskii functional and a stochastic analysis approach, some new delay-dependent sufficient conditions are obtained in the linear matrix inequality (LMI) format such that delayed MJSNNs are globally asymptotically stable in the mean-square sense for all admissible uncertainties. An important feature of the results is that the stability criteria are dependent on not only the lower bound and upper bound of delay for all modes but also the covariance matrix consisting of the correlation coefficient. Numerical examples are given to illustrate the effectiveness.

Key words: mode-dependent time-varying interval delay, multiplicative noise, covariance matrix, correlation coefficient, Markovian jumping stochastic neural networks

中图分类号:  (Stochastic analysis)

  • 02.50.Fz
02.30.Yy (Control theory) 02.50.Ga (Markov processes) 05.40.Ca (Noise) 05.40.Jc (Brownian motion)