Global Asymptotic Stability Analysis for Neural Networks with Time-Varying Delays

The problem of global asymptotic stability for a class of neural networks with variable delays is considered in this paper. Based on a more general Lyapunov-Krasovskii functional, a less conservative condition for global asymptotic stability is derived by using some slack matrix variables to express the relationship between the system matrices. The restriction on the derivative of the delay function to be less than unit is removed. A numerical example is given to illustrate the effectiveness of the proposed method

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

[2]  Vimal Singh,et al.  Global robust stability of delayed neural networks: an LMI approach , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Wang,et al.  Global stability and local stability of Hopfield neural networks with delays. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

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

[6]  Shengyuan Xu,et al.  Novel global asymptotic stability criteria for delayed cellular neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[7]  Guanrong Chen,et al.  Novel robust stability criteria for interval-delayed Hopfield neural networks , 2001 .

[8]  S. Arik.  Global robust stability of delayed neural networks , 2003 .

[9]  Jinde Cao,et al.  An estimation of upperbound of delays for global asymptotic stability of delayed Hopfield neural networks , 2002 .

[10]  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.

[11]  Tong Heng Lee,et al.  A less conservative robust stability test for linear uncertain time-delay systems , 2006, IEEE Trans. Autom. Control..

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

[13]  Min Wu,et al.  LMI-based stability criteria for neural networks with multiple time-varying delays , 2005 .

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

[15]  Jinde Cao,et al.  A delayed neural network for solving linear projection equations and its analysis , 2005, IEEE Transactions on Neural Networks.

[16]  Tianguang Chu,et al.  Exponential stability of neural networks with variable delays via LMI approach , 2006 .

[17]  Chuandong Li,et al.  Delay-dependent exponential stability analysis of bi-directional associative memory neural networks with time delay: an LMI approach , 2005 .

[18]  S. Arik.  An improved global stability result for delayed cellular neural networks , 2002 .

[19]  Sabri Arik,et al.  An analysis of exponential stability of delayed neural networks with time varying delays , 2004, Neural Networks.

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

[21]  Jinde Cao,et al.  Global robust stability of delayed recurrent neural networks , 2004 .

[22]  Jinde Cao.  A set of stability criteria for delayed cellular neural networks , 2001 .

[23]  Jinde Cao,et al.  A based-on LMI stability criterion for delayed recurrent neural networks , 2006 .