An LMI approach to asymptotical stability of multi-delayed neural networks

被引：74

作者：

Liao, XF ^{[1
]}

Li, CD ^{[1
]}

机构：

[1] Chongqing Univ, Dept Comp Sci & Engn, Chongqing 400044, Peoples R China

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2005年 / 200卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

neural networks; global asymptotic stability; Lyapunov-Krasovskii functional; linear matrix inequality; multiple time delays;

D O I：

10.1016/j.physd.2004.10.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, some criteria are derived for global asymptotic stability of a class of neural networks with multiple constant or time-varying delays. Based on the Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach, some delay-independent criteria for neural networks with multiple constant delays and delay-dependent criteria for neural networks with multiple time-varying delays are provided to guarantee global asymptotic stability of these networks. The main results are generalizations of some recent results reported in the literature. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：139 / 155

页数：17

共 28 条

[1] Stability analysis of delayed neural networks [J].

Arik, S .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 2000, 47 (07) :1089-1092

[2] HOW DELAYS AFFECT NEURAL DYNAMICS AND LEARNING [J].

BALDI, P ;

ATIYA, AF .

IEEE TRANSACTIONS ON NEURAL NETWORKS, 1994, 5 (04) :612-621

[3] Frustration, stability, and delay-induced oscillations in a neural network model [J].

Belair, J ;

Campbell, SA ;

VandenDriessche, P .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1996, 56 (01) :245-255

[4]

Belair J., 1993, Journal of Dynamics and Differential Equations, V5, P607, DOI 10.1007/BF01049141

[5]

Boy S., 1994, Linear MatrixInequalities in System and Control Theory

[6] DELAY-INDEPENDENT STABILITY IN BIDIRECTIONAL ASSOCIATIVE MEMORY NETWORKS [J].

GOPALSAMY, K ;

HE, XZ .

IEEE TRANSACTIONS ON NEURAL NETWORKS, 1994, 5 (06) :998-1002

[7] STABILITY IN ASYMMETRIC HOPFIELD NETS WITH TRANSMISSION DELAYS [J].

GOPALSAMY, K ;

HE, XZ .

PHYSICA D-NONLINEAR PHENOMENA, 1994, 76 (04) :344-358

[8] Delay induced periodicity in a neural netlet of excitation and inhibition [J].

Gopalsamy, K ;

Leung, I .

PHYSICA D, 1996, 89 (3-4) :395-426

[9]

HALE JK, 1991, INTRO THEORY FUNCTIO

[10] NEURONS WITH GRADED RESPONSE HAVE COLLECTIVE COMPUTATIONAL PROPERTIES LIKE THOSE OF 2-STATE NEURONS [J].

HOPFIELD, JJ .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-BIOLOGICAL SCIENCES, 1984, 81 (10) :3088-3092

← 1 2 3 →