Stability Analysis of Delay Neural Networks With Impulsive Effects

A generalized model of neural networks with time-varying delays and impulsive effects is considered. By establishing an impulsive delay differential inequality, we investigate the global exponential stability and uniform stability of impulsive delay neural networks. Our sufficient conditions ensuring the stability are dependent on delays and impulses and show delay and impulsive effects on the stability of neural networks. The results extend and improve the earlier publications.

[1]  Daoyi Xu,et al.  Global dynamics of Hopfield neural networks involving variable delays , 2001 .

[2]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[3]  Jun Wang,et al.  Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays , 2003 .

[4]  Qidi Wu,et al.  Less conservative conditions for asymptotic stability of impulsive control systems , 2003, IEEE Trans. Autom. Control..

[5]  Johan A. K. Suykens,et al.  Master-Slave Synchronization of Lur'e Systems with Time-Delay , 2001, Int. J. Bifurc. Chaos.

[6]  A. N. Michel,et al.  Stability analysis of systems with impulse effects , 1998, IEEE Trans. Autom. Control..

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

[8]  Michael A. Arbib,et al.  Brains, machines and mathematics (2. ed.) , 1987 .

[9]  Tao Yang,et al.  Impulsive Systems and Control: Theory and Applications , 2001 .

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

[11]  Guanrong Chen,et al.  On delayed impulsive Hopfield neural networks , 1999, Neural Networks.

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

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

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

[15]  C. W. Chan,et al.  Robust stabilization of singular-impulsive-delayed systems with nonlinear perturbations , 2001 .

[16]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[17]  Amir F. Atiya,et al.  How delays affect neural dynamics and learning , 1994, IEEE Trans. Neural Networks.

[18]  D. Baĭnov,et al.  Systems with impulse effect : stability, theory, and applications , 1989 .

[19]  Wassim M. Haddad,et al.  Nonlinear impulsive dynamical systems. I. Stability and dissipativity , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[20]  H. Akça,et al.  Continuous-time additive Hopfield-type neural networks with impulses , 2004 .

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

[22]  J. Suykens,et al.  Impulsive Synchronization of Chaotic Lur'e Systems by Measurement Feedback , 1998 .

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