New global asymptotic stability criterion for neural networks with discrete and distributed delays

Abstract

This paper investigates the problem of global asymptotic stability for a class of neural networks with time-varying and distributed delays. By the Lyapunov-Krasovskii functional approach, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). The new stability condition does not require the time delay function to be continuously differentiable and its derivative to be less than 1, and it allows the time delay to be a fast time-varying function. Simulation examples are given to demonstrate the effectiveness of the developed techniques.

Keywords

neural networks time-varying delay distributed delay global asymptotic stability linear matrix inequalities

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References

Boukas

Liu

Shi

Delay-dependent stability and output feedback stabilization of Markov jump systems with time-delay

IEE-Part D, Control Theory and Applic., 2002, 149 (5), 379–386.

Mahmoud

Shi

Methodologies for control of jump time-delay systems, 2003 (Kluwer Academic Publishers, Boston, Massachusetts).

Boukas

E. K.

Al-Muthairi

N. F.

Delaydependent stabilization of singular linear systems with delays

Int. J. Innovative Comput. Inf. Control, 2006, 2 (2), 283–291.

Chen

Lam

Memory state feedback guaranteed cost control for neutral delay systems

Int. J. Innovative Comput. Inf. Control, 2006, 2 (2), 293–303.

Liao

Chen

Sanchez

E. N.

Delaydependent exponential stability analysis of delayed neural networks: An LMI approach

Neural Networks, 2002, 15, 855–866.

Yang

Chu

Zhang

Exponential stability of neural networks with variable delays via LMI approach

Chaos, Solitons and Fractals, 2006, 30 (1), 133–139.

Lam

D. W. C.

Zou

Delaydependent exponential stability for a class of neural networks with time delays

J. Comput. and Appl. Math., 2005, 183, 16–28.

Zhang

Wei

Delay-dependent exponential stability of cellular neural networks with time-varying delays

Chaos, Solitons and Fractals, 2005, 23 (4), 1363–1369.

Liao

Zhang

Delay-dependent asymptotic stability of a two-neuron system with different time delays

Chaos, Solitons and Fractals, 2006, 28, 437–447.

10.

Wang

LMI-based stability criteria for neural networks with multiple time-varying delays

Phys. D, 2005, 212, 126–136.

11.

Cao

Wang

Delay-dependent robust stability of uncertain nonlinear systems with time delay

Appl. Math. and Computation, 2004, 154, 289–297.

12.

Chen

W.-H.

Guan

Z.-H.

Delay-dependent exponential stability of neural networks with variable delays

Phys. Lett. A, 2004, 326, 355–363.

13.

Zhao

Global asymptotic stability of Hopfield neural network involving distributed delays

Neural Networks, 2004, 17 (1), 47–53.

14.

Wang

Liu

On global asymptotic stability of neural networks with discrete and distributed delays

Phys. Lett. A, 2005, 345 (4-6), 299–308.

15.

Kolmanovskii

V. B.

Myshkis

A. D.

Applied theory of functional differential equations, 1992 (Kluwer Academic Publishers, Dordrecht).

16.

Gopalsamy

Stability in asymmetric Hopfield nets with transmission delays

Phys. D, 1994, 76 (4), 344–358.

17.

Boyd

El Ghaoui

Feron

Balakrishnan

Linear matrix inequalities in system and control theory, 1994 (SIAM, Philadelphia, Pennsylvania).

18.

Hale

Lunel

Verduyn S. M.

Introduction to functional differential equations, 1993 (Springer-Verlag, New York).

19.

Rios-Patron

Braatz

R. D.

Robust nonlinear control of a pH neutralization process. In Proceedings of the American Control Conference, San Diego, California, pp. 119–123, 1999 (American Automatic Control Council).

20.

Arik

Stability analysis of delayed neural networks, IEEE Trans. Circuits Syst.-I, Vol. 47, no. 7, pp. 1089–1092, 2000.