Exponential Stability of Cellular Neural Networks with Uncertain and Time-Varying Delay

A novel method is proposed in this note for exponential stability of cellular neural networks with uncertain and time-varying delay. New delay-dependent exponential stability conditions of cellular neural network with time-varying delay is presented by constructing Lyapunov function and using linear matrix inequality (LMI). The sufficient conditions on exponential stability established in this paper, which are easily verifiable, have a wider adaptive range. Finally, a numerical example is given to demonstrate the effect of the proposed method.

I. Introduction

The Cellular Neural Networks (CNNs) introduced by Chua and Yang, have been extensively investigated due to their important applications in such fields as image processing and pattern recognition. Reference[1] presented the delayed version of CNNs. A number of applications of CNN s have emerged. This paper proposes a novel linear matrix inequality (LMI)-based criterion for the exponential stability. So far, most of these existing results for the global asymptotic stability of the delayed cellular neural networks are independent of the delay parameters [2],[3],[4],[5],[6]. However, how to propose a delay-dependent stability criterion for delayed cellular neural networks is an open problem [7],[8],[9].