Stability analysis for delayed neural networks via an improved negative-definiteness lemma

This article studies the stability problem for neural networks with a time-varying delay. An improved negative-definiteness lemma (NDL) is proposed by removing some redundant inequality constraints involved in the original one that is recently developed via a quadratic-partitioning method. Furthermore, the improved NDL is presented in the matrix-valued form for convenient application. With regard to the case that the upper bound of the variation of the delay is less than a known constant while the lower bound is unknown, an appropriate Lyapunov-Krasovskii functional (LKF) candidate is deliberately built so that the derivative of the LKF is estimated to be a novel quadratic function with respect to the delay. Consequently, a series of new stability criteria is obtained via the improved NDL, which is shown to be less conservative than existing ones through numerical examples. (c) 2021 Published by Elsevier Inc.