Asymptotic Stability of a Delay-Difference Control System of Hopfield Neural Networks via Matrix Inequalities and Applications

Kreangkri RATCHAGIT

Authors

Kreangkri RATCHAGIT Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290

Keywords:

Hopfield neural networks, delay-difference control system, asymptotic stability, lyapunov function, matrix inequalities

Abstract

We have established a new sufficient condition for the asymptotic stability of a delay-difference control system of Hopfield neural networks in terms of certain matrix inequalities (based on a discrete analog of the Lyapunov second method). The result has been applied to obtain new stability conditions for some class of delay-difference control system such as delay-difference control system of Hopfield neural networks with multiple delays in terms of certain matrix inequalities.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

References

XZ Liu, Y Liu and KL Teo. Stability analysis of impulsive control systems. Math. Comput. Model. 2003; 37, 1357-70.

S Elaydi and A Peterson. Difference Equations. Academic Press, New York, 1990.

S Arik. Global robust stability analysis of the neural networks with discrete time delays. Chaos Soliton Fract. 2005; 26, 1407-14.

MM Gubta and L Jin. Globally asymptotical stability of discrete-time analog neural networks. IEEE T. Neural Networ. 1996; 7, 1024-31.

LO Chua and L Yang. Cellular neural networks. IEEE T. Circuits Syst. 1988; 35, 1273-90.

TA Burton. Averaged neural networks. Neural Networks 1993; 6, 677-80.

H Ye. Global stability and local stability of Hopfield neural networks with delay. Phys. Rev. 1944; 50, 4208-15.

RP Agarwal. Difference Equations and Inequalities. Marcel Dekker Inc., New York, 1992.

K Gu. An integral inequality in the stability problem of time-delay systems. In: Proceedings of the 39th IEEE CDC Conf., Sydney, Australia. 2000, p. 2805-10.

J Hale. Theory of The Functional Differential Equations. Springer-Verlag, New York, 1977.

S Hu and J Wang. Global stability of a class of discrete-time recurrent neural networks. IEEE T. Circuits-I 2006; 49, 1021-29.

F Callier and CA Desoer. Linear System Theory. Hong Kong, Springer-Verlag, 1992.

EF Infante. A Lyapunov functional for the matrix difference-differential equation. J. Differ. Equations 1981; 35, 261-4.

K Ratchagit. Asymptotic stability of delay difference system of the Hopfield neural networks via matrix inequalities and application. Int. J. Neural Syst. 2007; 17, 425-30.

XP Wei, J Xu and Q Zang. New stability conditions for neural networks with constant and variable delays. Chaos Solition Fract. 2005; 26, 1391-98.