On the Global Dissipativity of a Class of Cellular Neural Networks with Multipantograph Delays

Liqun Zhou

doi:10.1155/2011/941426

Abstract

For the first time the global dissipativity of a class of cellular neural networks with multipantograph delays is studied. On the one hand, some delay‐dependent sufficient conditions are obtained by directly constructing suitable Lyapunov functionals; on the other hand, firstly the transformation transforms the cellular neural networks with multipantograph delays into the cellular neural networks with constant delays and variable coefficients, and then constructing Lyapunov functionals, some delay‐independent sufficient conditions are given. These new sufficient conditions can ensure global dissipativity together with their sets of attraction and can be applied to design global dissipative cellular neural networks with multipantograph delays and easily checked in practice by simple algebraic methods. An example is given to illustrate the correctness of the results.

Highlights

In recent years, cellular neural networks (CNNs) and delayed cellular neural networks (DCNNs) have been investigated widely because of their extensive applications in pattern recognition, image processing, association, synchronization problem, and many other fields
Consider the model of multipantograph delayed CNNs described by the following functional differential equations: n xi(t) = −dixi(t) + aij fj xj (t) + bij fj xj q1t j=1
The pantograph delay systems as an important mathematical models often arise in some fields such as physics, biology systems, and control theory

Summary

Introduction

Cellular neural networks (CNNs) and delayed cellular neural networks (DCNNs) have been investigated widely because of their extensive applications in pattern recognition, image processing, association, synchronization problem, and many other fields. In such applications, it is of prime importance to ensure that the designed CNNs be stable. The main contributions of this paper include the derivations of new global attractive sets and characterization of global dissipativity These properties play important roles in the design and applications of global dissipative CNNs with multipantograph delays, and are of great interest in many applications, such as chaos and synchronization theory, and robust control

Model and Preliminaries

Main Results

Examples

Conclusions