Criteria for exponential stability of Cohen-Grossberg neural networks

被引：171
作者：
Liao, XF [1 ]
Li, CG
Wong, KW
机构：
[1] Chongqing Univ, Dept Comp Engn & Sci, Chongqing 400044, Peoples R China
[2] Univ Elect Sci & Technol China, Lab 570, Coll Elect Engn, Chengdu 610054, Peoples R China
[3] City Univ Hong Kong, Dept Comp Engn & Informat Technol, Kowloon, Hong Kong, Peoples R China
来源：
NEURAL NETWORKS | 2004年 / 17卷 / 10期
基金：
中国国家自然科学基金;
关键词：
global exponential stability; Cohen-Grossberg model; neural networks; Lyapunov functionals;
D O I：
10.1016/j.neunet.2004.08.007
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper. the Cohen-Grossberg neural network models without and with time delays are considered. By constructing several novel Lyapunov functionals, some sufficient criteria for the existence of a unique equilibrium and global exponential stability of the network are derived. These results are fairly general and can be easily verified. Besides, the approach of the analysis allows one to consider different types of activation functions, including piecewise linear, sigmoids with bounded activations as well as C-1-smooth sigmoids. In the meantime, our approach does not require any symmetric assumption of the connection matrix. It is believed that these results are significant and useful for the design and applications of the Cohen-Grossberg model. (C) 2004 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1401 / 1414
页数：14
相关论文
共 22 条
[1]   ABSOLUTE STABILITY OF GLOBAL PATTERN-FORMATION AND PARALLEL MEMORY STORAGE BY COMPETITIVE NEURAL NETWORKS [J].
COHEN, MA ;
GROSSBERG, S .
IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS, 1983, 13 (05) :815-826
[2]   ON GLOBAL ASYMPTOTIC STABILITY OF A CLASS OF NONLINEAR-SYSTEMS ARISING IN NEURAL-NETWORK THEORY [J].
FORTI, M .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 113 (01) :246-264
[3]   DELAY-INDEPENDENT STABILITY IN BIDIRECTIONAL ASSOCIATIVE MEMORY NETWORKS [J].
GOPALSAMY, K ;
HE, XZ .
IEEE TRANSACTIONS ON NEURAL NETWORKS, 1994, 5 (06) :998-1002
[4]   STABILITY IN ASYMMETRIC HOPFIELD NETS WITH TRANSMISSION DELAYS [J].
GOPALSAMY, K ;
HE, XZ .
PHYSICA D-NONLINEAR PHENOMENA, 1994, 76 (04) :344-358
[5]   NONLINEAR NEURAL NETWORKS - PRINCIPLES, MECHANISMS, AND ARCHITECTURES [J].
GROSSBERG, S .
NEURAL NETWORKS, 1988, 1 (01) :17-61
[6]  
HOPFIELD JJ, 1984, P NATIONAL ACADEMY S, V81, P3058
[7]   Results concerning the absolute stability of delayed neural networks [J].
Joy, M .
NEURAL NETWORKS, 2000, 13 (06) :613-616
[8]   LMI-Based approach for asymptotically stability analysis of delayed neural networks [J].
Liao, XF ;
Chen, GR ;
Sanchez, EN .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2002, 49 (07) :1033-1039
[9]   Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach [J].
Liao, XF ;
Chen, GR ;
Sanchez, EN .
NEURAL NETWORKS, 2002, 15 (07) :855-866
[10]   Novel robust stability criteria for interval-delayed Hopfield neural networks [J].
Liao, XF ;
Wong, KW ;
Wu, ZF ;
Chen, GR .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 2001, 48 (11) :1355-1359
123