Resilient H∞ synchronization of piecewise-homogeneous markovian jumping NNs with time-varying delay and asynchronous modes: A delayed event-triggered scheme

This article is devoted to addressing the resilient asynchronous $H_{\infty }$ synchronization problem for piecewise-homogeneous Markovian jumping neural networks (NNs) with time-varying delay. Specifically, the presented NNs are modeled as a piecewise-homogeneous Markovian jumping system, which means that the system parameters and structure remain unchanged within each fixed time interval, although significant differences may exist between intervals. In other words, this piecewise-homogeneous approach lies between homogeneous and non-homogeneous methods. Besides, in order to cut down on communication waste and enhance the utilization of resources, an innovative delayed event-triggered approach is put forward, which availably avoid Zeno phenomenon and optimize trigger performance. By employing stochastic analysis technique, Lyapunov stability theory, and matrix inequality methods, certain sufficient criteria for achieving mean-square global asymptotic stability of error system are derived. Additionally, the desired gains can be explicitly designed by solving the corresponding matrix inequalities. Finally, one numerical simulation example is presented to reveal the viability and effectiveness of suggested event-triggered approach.