Robust Stability Analysis of Uncertain Stochastic Neural Networks with Time-Varying Delays

This paper is concerned with stochastic robust stability of a class of stochastic neural networks with time varying delays and parameter uncertainties. The parameter uncertainties are time-varying and norm-bounded. Based on Lyapunov-Krasovskii functional and stochastic analysis approaches, new stability criteria are presented in terms of linear matrix inequalities (LMIs) to guarantee the delayed neural network to be robustly stochastically asymptotically stable in the mean square for all admissible uncertainties. Numerical examples are given to demonstrate the usefulness of the proposed robust stability criteria.

[1]  S. Arik.  Stability analysis of delayed neural networks , 2000 .

[2]  Xinzhi Liu,et al.  Robust Stability of Uncertain Discrete Impulsive Systems , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Sabri Arik,et al.  An analysis of global asymptotic stability of delayed cellular neural networks , 2002, IEEE Trans. Neural Networks.

[4]  Shun-ichi Amari,et al.  Stability of asymmetric Hopfield networks , 2001, IEEE Trans. Neural Networks.

[5]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[6]  G. Feng,et al.  Delay-dependent stability for uncertain stochastic neural networks with time-varying delay , 2007 .

[7]  Xuerong Mao,et al.  Stability of stochastic neural networks , 1996, Neural Parallel Sci. Comput..

[8]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .

[9]  Zidong Wang,et al.  Robust stability for stochastic Hopfield neural networks with time delays , 2006 .

[10]  Xuerong Mao,et al.  Exponential stability and instability of stochastic neural networks 1 , 1996 .

[11]  Jianhua Sun,et al.  Mean square exponential stability of stochastic delayed Hopfield neural networks , 2005 .

[12]  Xuerong Mao,et al.  Stability of stochastic delay neural networks , 2001, J. Frankl. Inst..

[13]  Jin-Hoon Kim,et al.  Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty , 2001, IEEE Trans. Autom. Control..