A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach

In this paper, global asymptotic stability is discussed for neural networks with time-varying delay. Several new criteria in matrix inequality form are given to ascertain the uniqueness and global asymptotic stability of equilibrium point for neural networks with time-varying delay based on Lyapunov method and Linear Matrix Inequality (LMI) technique. The proposed LMI approach has the advantage of considering the difference of neuronal excitatory and inhibitory efforts, which is also computationally efficient as it can be solved numerically using recently developed interior-point algorithm. In addition, the proposed results generalize and improve previous works. The obtained criteria also combine two existing conditions into one generalized condition in matrix form. An illustrative example is also given to demonstrate the effectiveness of the proposed results.

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

[2]  Jinde Cao.  Periodic oscillation and exponential stability of delayed CNNs , 2000 .

[3]  Marco Gilli,et al.  Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions , 1994 .

[4]  Jinde Cao,et al.  Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays , 2004 .

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

[6]  Kwong-Sak Leung,et al.  Convergence analysis of cellular neural networks with unbounded delay , 2001 .

[7]  Jinde Cao,et al.  Stability analysis of delayed cellular neural networks , 1998, Neural Networks.

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

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

[10]  S. Arik,et al.  On the global asymptotic stability of delayed cellular neural networks , 2000 .

[11]  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.

[12]  Hongtao Lu,et al.  On stability of nonlinear continuous-time neural networks with delays , 2000, Neural Networks.

[13]  Réjean Plamondon,et al.  On the stability analysis of delayed neural networks systems , 2001, Neural Networks.

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

[15]  Jinde Cao.  Global stability conditions for delayed CNNs , 2001 .

[16]  Jinde Cao,et al.  Globally exponentially robust stability and periodicity of delayed neural networks , 2004 .

[17]  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.

[18]  Teh-Lu Liao,et al.  Global stability for cellular neural networks with time delay , 2000, IEEE Trans. Neural Networks Learn. Syst..

[19]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[20]  J. Hopfield,et al.  Computing with neural circuits: a model. , 1986, Science.

[21]  E. Feron,et al.  History of linear matrix inequalities in control theory , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[22]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[23]  S. Arik,et al.  Equilibrium analysis of delayed CNNs , 1998 .

[24]  Kwok-Wo Wong,et al.  Asymptotic stability criteria for a two-neuron network with different time delays , 2003, IEEE Trans. Neural Networks.

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

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

[27]  Leon O. Chua,et al.  Cellular neural networks with non-linear and delay-type template elements and non-uniform grids , 1992, Int. J. Circuit Theory Appl..

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

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

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

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

[32]  Q. Henry Wu,et al.  A note on stability of analog neural networks with time delays , 1996, IEEE Trans. Neural Networks.

[33]  Jinde Cao,et al.  Periodic solutions and exponential stability in delayed cellular neural networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[34]  Leon O. Chua,et al.  Stability of cellular neural networks with dominant nonlinear and delay-type templates. (Memo UCB/ERL No. M92/121.) , 1993 .

[35]  Norikazu Takahashi,et al.  A new sufficient condition for complete stability of cellular neural networks with delay , 2000 .

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

[37]  Jinde Cao,et al.  Global exponential stability of Hopfield neural networks , 2001, Int. J. Syst. Sci..

[38]  Jun Wang,et al.  An additive diagonal-stability condition for absolute exponential stability of a general class of neural networks , 2001 .

[39]  Mauro Forti.  Some extensions of a new method to analyze complete stability of neural networks , 2002, IEEE Trans. Neural Networks.

[40]  Anthony N. Michel,et al.  A synthesis procedure for Hopfield's continuous-time associative memory , 1990 .

[41]  Kwok-Wo Wong,et al.  Novel stability conditions for Cellular Neural Networks with Time Delay , 2001, Int. J. Bifurc. Chaos.

[42]  Jinde Cao,et al.  Exponential stability and periodic oscillatory solution in BAM networks with delays , 2002, IEEE Trans. Neural Networks.