Exponential stability of neural networks with variable delays via LMI approach

This paper presents sufficient conditions for global asymptotic/exponential stability of neural networks with time-varying delays. By using appropriate Lyapunov–Krasovskii functionals, we derive stability conditions in terms of linear matrix inequalities (LMIs). This is convenient for numerically checking the system stability using the powerful MATLAB LMI Toolbox. Compared with some earlier work, our result does not require any restriction on the derivative of the delay function. Numerical example shows the efficiency and less conservatism of the present result.

[1]  Xue-Zhong He,et al.  Delay-independent stability in bidirectional associative memory networks , 1994, IEEE Trans. Neural Networks.

[2]  V. Singh,et al.  Global asymptotic stability of cellular neural networks with unequal delays: LMI approach , 2004 .

[3]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[4]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[5]  Guanrong Chen,et al.  LMI-based approach for asymptotically stability analysis of delayed neural networks , 2002 .

[6]  Leon O. Chua,et al.  Stability and dynamics of delay-type general and cellular neural networks , 1992 .

[7]  Qiang Zhang,et al.  Global asymptotic stability of Hopfield neural networks with transmission delays , 2003 .

[8]  LiaoXiaofeng,et al.  Delay-dependent exponential stability analysis of delayed neural networks , 2002 .

[9]  L. Pandolfi,et al.  On stability of cellular neural networks with delay , 1993 .

[10]  Long Wang,et al.  Exponential convergence estimates for neural networks with multiple delays , 2002 .

[11]  Wang,et al.  Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  T. Chu,et al.  A decomposition approach to analysis of competitive–cooperative neural networks with delay , 2003 .

[13]  Tianguang Chu,et al.  An exponential convergence estimate for analog neural networks with delay , 2001 .

[14]  Jiye Zhang.  Globally exponential stability of neural networks with variable delays , 2003 .

[15]  Chien-Yu Lu,et al.  Stability of cellular neural networks with time-varying delay , 2003 .

[16]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[17]  S. Arik,et al.  New exponential stability results for delayed neural networks with time varying delays , 2004 .

[18]  Qian Jixin,et al.  Stability analysis for neural dynamics with time-varying delays , 1998, IEEE Trans. Neural Networks.

[19]  Vimal Singh,et al.  A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks , 2004, IEEE Transactions on Neural Networks.

[20]  Pauline van den Driessche,et al.  Global Attractivity in Delayed Hopfield Neural Network Models , 1998, SIAM J. Appl. Math..

[21]  Mark P. Joy,et al.  Results concerning the absolute stability of delayed neural networks , 2000, Neural Networks.

[22]  Xiaofeng Liao,et al.  (Corr. to) Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach , 2002, Neural Networks.