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Circuits Syst Signal Process (2014) 33:10671094
DOI 10.1007/s00034-013-9677-1
Global Stability of Fuzzy Cellular Neural Networks with Mixed Delays and Leakage Delay Under Impulsive Perturbations
Cheng-De Zheng Yan Wang Zhanshan Wang
Received: 6 May 2013 / Revised: 10 September 2013 / Published online: 11 October 2013 Springer Science+Business Media New York 2013
Abstract This paper investigates the global asymptotic stability of a kind of fuzzy cellular neural networks with mixed delays under impulsive perturbations. The mixed delays include constant delay in the leakage term (i.e., leakage delay), time-varying delays, and continuously distributed delays. By using the quadratic convex combination method, reciprocal convex approach, Jensen integral inequality, and linear convex combination technique, several novel sufcient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.
Keywords Impulse Fuzzy neural networks Reciprocal convex technique
Quadratic convex combination Linear convex combination
1 Introduction
It is well known that recurrent neural networks have been extensively studied and successfully applied in many areas such as associative memory, optimization problem, xed point computations, combinatorial optimization, pattern recognition, signal processing, static processing, and so on. Usually, a time delay occurs in these neural networks, and this makes a difference to their stability [9, 1315, 20, 21, 2528, 30].
C.-D. Zheng (
B) Y. Wang
School of Science, Dalian Jiaotong University, Dalian 116028, P.R. China e-mail: [email protected]
Z. WangSchool of Information Science and Engineering, Northeastern University, Shenyang 110004, P.R. China
1068 Circuits Syst Signal Process (2014) 33:10671094
Most models of cellular neural networks are variations of the following system of differential equations:
xi(t) = dixi(t) +
n
j=1
aijfj xj (t) +
n
j=1
bijfj xj t (t) + i, (1)
where the rst term in the right side of (1) corresponds to a stabilizing negative feedback of the system, which acts instantaneously without time delay; this term is variously known as forgetting or leakage term (see, for instance, [7]). It is known from the literature on population dynamics (see Gopalsamy [2]) that time delay...