Stability Analysis for Neural Networks with Time-Variable Delays

In this paper, the stability of neural networks (NNs) with time-varying delays is investigated. By introducing a new Lyapunov-Krasovskii functional in virtue of the linearization of the model under investigation and considering the additional useful terms when estimating the upper bound of the derivative of Lyapunov functional, a new delay-dependent stability criterion is established in term of linear matrix inequality (LMI). Some numerical simulation examples aimed at justifying the theoretical results are also given.

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

[2]  Jinde Cao,et al.  Global exponential stability and periodicity of recurrent neural networks with time delays , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[3]  Min Wu,et al.  An improved global asymptotic stability criterion for delayed cellular neural networks , 2006, IEEE Transactions on Neural Networks.

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

[5]  Xin-Ping Guan,et al.  Stability of Cellular Neural Networks with Time Varying Delay , 2010, 2008 Fourth International Conference on Natural Computation.

[6]  Jinde Cao,et al.  Almost periodic attractor of delayed neural networks with variable coefficients , 2005 .

[7]  J. Lam,et al.  Novel global robust stability criteria for interval neural networks with multiple time-varying delays , 2005 .

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

[9]  Hongye Su,et al.  New results on robust exponential stability for discrete recurrent neural networks with time-varying delays , 2009, Neurocomputing.

[10]  Yun Zou,et al.  Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays , 2008, Neurocomputing.

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

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

[13]  Jinde Cao,et al.  Global exponential stability of discrete-time Cohen-Grossberg neural networks , 2005, Neurocomputing.

[14]  Qing-Long Han,et al.  New Lyapunov-Krasovskii Functionals for Global Asymptotic Stability of Delayed Neural Networks , 2009, IEEE Trans. Neural Networks.

[15]  Chuandong Li,et al.  An LMI approach to asymptotical stability of multi-delayed neural networks , 2005 .

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

[17]  J. Qiu,et al.  New robust stability criteria for uncertain neural networks with interval time-varying delays , 2009 .

[18]  Wang Lin-shan Global Robust Stability of Interval Cellular Neural Networks with Time-varying Delays , 2004 .

[19]  G.P. Liu,et al.  Nonlinear Identification and Control: A Neural Network Approach [Book Review] , 2002, IEEE Control Systems.

[20]  Sabri Arik,et al.  Global stability of a class of neural networks with time-varying delay , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[21]  Jinde Cao,et al.  Global robust stability of interval neural networks with multiple time-varying delays , 2007, Math. Comput. Simul..

[22]  Jinde Cao,et al.  A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach , 2005 .

[23]  E. Sánchez,et al.  Input-to-state stability (ISS) analysis for dynamic neural networks , 1999 .

[24]  Qiang Zhang,et al.  Delay-dependent exponential stability of cellular neural networks with time-varying delays , 2005 .

[25]  T. Liao,et al.  Globally exponential stability condition of a class of neural networks with time-varying delays , 2005 .

[26]  Chuandong Li,et al.  Delay-Dependent and Delay-Independent Stability Criteria for Cellular Neural Networks with Delays , 2006, Int. J. Bifurc. Chaos.

[27]  V. Singh Robust stability of cellular neural networks with delay: linear matrix inequality approach , 2004 .

[28]  Zidong Wang,et al.  A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays , 2007 .

[29]  Wei Xing Zheng,et al.  A new approach to stability analysis of discrete-time recurrent neural networks with time-varying delay , 2009, Neurocomputing.