Stability Analysis for Neural Networks With Time-Varying Delay Based on Quadratic Convex Combination

In this paper, a novel method is developed for the stability problem of a class of neural networks with time-varying delay. New delay-dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time-varying delay are derived by the newly proposed augmented simple Lyapunov-Krasovski functional. Different from previous results by using the first-order convex combination property, our derivation applies the idea of second-order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to Jensen's inequality. A numerical example is provided to verify the effectiveness and superiority of the presented results.

I. Introduction

Neural networks belong to a special class of nonlinear dynamical systems, and much attention has been paid to them in the past few decades because of their extensive applications, such as in pattern recognition [1], combinatorial optimization [2], associative memory [3], and so forth. It is sometimes desirable to introduce delays into neural networks when dealing with problems associated with motions [4]. On the other hand, since the neural nets are usually implemented by different hardware circuits—analog, digital, or even very large scale integrated circuits—time delay is inevitably encountered in their electronic implementation due to the finite switching speed of amplifier when information is processed and signals are transmitted; this is frequently a source of oscillation or instability in neural networks [5]. Therefore, the stability of neural networks with delay has become a topic of great theoretical and practical importance.