Stability analysis for impulsive neural networks with variable delays

The problem of global exponential stability analysis of impulsive neural networks with variable delays is investigated in this paper. The cases of impulses considered in this paper include that (1) the impulses are input disturbance; (2) the impulses are “neutral” type (that is, they are neither helpful for stability for neural networks nor destabilizing). A new approach based on Lyapunov function and Razumikhin-type techniques is developed to establish delay-independent sufficient conditions for global exponential stability in each case of impulses. These new stability conditions are expressed in form of linear matrix inequalities with regard to proper types of impulse time sequences and are independent of the size of variable delays. The effectiveness of the new results are further illustrated by numerical examples.

I. Introduction

During the last twenty years, the stability of neural networks with time delays has been an active area of research due to its importance in many applications such as signal processing, associative memory, pattern recognition, and analog circuits. As a result, a considerable number of stability criteria for delayed neural networks have been proposed (see, e.g., [3], [4], [6], [14], [20]).