A Switched System Model for Exponential Stability and Dissipativity of Delayed Neural Networks
Hong‐Bing Zeng, Zong-Jun Zhu, Shen-Ping Xiao, Xian‐Ming Zhang
Abstract
This article investigates the problems of exponential stability and dissipativity for neural networks with time-varying delays. To capture more information on the delay and its derivative in constructing Lyapunov-Krasovskii functionals (LKFs), the original delayed neural network (DNN) is modeled as a switching system with two modes, corresponding to cases where the delay derivative is positive or negative. This model provides extra freedom in constructing a proper LKF, allowing for the selection of different Lyapunov matrices in each mode. By applying the average dwell time (ADT) technique, several criteria for exponential stability and exponential dissipativity are obtained for DNNs. Two extensively studied benchmark examples and a quadruple-tank process control system are provided to demonstrate the superiority of the proposed criteria over some existing methods and to verify the practical applicability of the approach.