Improved Stability Criteria for Delayed Neural Networks Using a Quadratic Function Negative-Definiteness Approach

Abstract

This brief is concerned with the stability of a neural network with a time-varying delay using the quadratic function negative-definiteness approach reported recently. A more general reciprocally convex combination inequality is taken to introduce some quadratic terms into the time derivative of a Lyapunov-Krasovskii (L-K) functional. As a result, the time derivative of the L-K functional is estimated by a novel quadratic function on the time-varying delay. Moreover, a simple way is introduced to calculate the coefficients of a quadratic function, which avoids tedious works by hand as done in some studies. The L-K functional approach is applied to derive a hierarchical type stability criterion for the delayed neural networks, which is of less conservatism in comparison with some existing results through two well-studied numerical examples.