Global exponential stability of impulsive high-order BAM neural networks with time-varying delays

In this paper, global exponential stability and exponential convergence are studied for a class of impulsive high-order bidirectional associative memory (BAM) neural networks with time-varying delays. By employing linear matrix inequalities (LMIs) and differential inequalities with delays and impulses, several sufficient conditions are obtained for ensuring the system to be globally exponentially stable. Three illustrative examples are also given at the end of this paper to show the effectiveness of our results.

[1]  M. Forti,et al.  Global convergence of neural networks with discontinuous neuron activations , 2003 .

[2]  P.K. Simpson,et al.  Higher-ordered and intraconnected bidirectional associative memories , 1990, IEEE Trans. Syst. Man Cybern..

[3]  B Kosko,et al.  Adaptive bidirectional associative memories. , 1987, Applied optics.

[4]  Marios M. Polycarpou,et al.  High-order neural network structures for identification of dynamical systems , 1995, IEEE Trans. Neural Networks.

[5]  Jiye Zhang,et al.  Global stability analysis of bidirectional associative memory neural networks with time delay , 2001, Int. J. Circuit Theory Appl..

[6]  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.

[7]  Jinde Cao,et al.  Existence and stability of almost periodic solution for BAM neural networks with delays , 2003, Appl. Math. Comput..

[8]  Pierre Baldi,et al.  Neural networks, orientations of the hypercube, and algebraic threshold functions , 1988, IEEE Trans. Inf. Theory.

[9]  S. Mohamad.  Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks , 2001 .

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

[11]  Hongyong Zhao.  Global stability of bidirectional associative memory neural networks with distributed delays , 2002 .

[12]  Santosh S. Venkatesh,et al.  The capacity of the Hopfield associative memory , 1987, IEEE Trans. Inf. Theory.

[13]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[14]  Jinde Cao,et al.  Exponential stability of high-order bidirectional associative memory neural networks with time delays , 2004 .

[15]  Demetri Psaltis,et al.  Higher order associative memories and their optical implementations , 1988, Neural Networks.

[16]  Changyun Wen,et al.  Impulsive control for the stabilization and synchronization of Lorenz systems , 2000 .

[17]  Manolis A. Christodoulou,et al.  Structural properties of gradient recurrent high-order neural networks , 1995 .

[18]  K. Gopalsamy,et al.  Stability of artificial neural networks with impulses , 2004, Appl. Math. Comput..

[19]  Jinde Cao,et al.  Global asymptotic stability of delayed bi-directional associative memory neural networks , 2003, Appl. Math. Comput..

[20]  R. D. Driver,et al.  Ordinary and Delay Differential Equations , 1977 .

[21]  Qidi Wu,et al.  Impulsive control for the stabilization and synchronization of Lorenz systems , 2002 .

[22]  Jinde Cao,et al.  Globally exponential stability conditions for cellular neural networks with time-varying delays , 2002, Appl. Math. Comput..

[23]  D. Yue,et al.  Differential inequality with delay and impulse and its applications to design of robust control , 1999 .

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

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

[26]  A. Dembo,et al.  High-order absolutely stable neural networks , 1991 .

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

[28]  Juebang Yu,et al.  Qualitative analysis of Bi‐directional Associative Memory with time delay , 1998 .

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

[30]  Jinde Cao,et al.  An analysis of periodic solutions of bi-directional associative memory networks with time-varying delays , 2004 .

[31]  Zhi-Hong Guan,et al.  On impulsive autoassociative neural networks , 2000, Neural Networks.

[32]  Isabelle Guyon,et al.  High-order neural networks: information storage without errors , 1987 .

[33]  Jinde Cao,et al.  Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays , 2004, Neural Networks.

[34]  Jinde Cao,et al.  Exponential stability of delayed bi-directional associative memory networks , 2003, Appl. Math. Comput..

[35]  Bingji Xu,et al.  Global asymptotic stability of high-order Hopfield type neural networks with time delays , 2003 .

[36]  H. Antosiewicz,et al.  Differential Equations: Stability, Oscillations, Time Lags , 1967 .