Event-triggered reachable set estimation for synchronization of Markovian jump complex-valued delayed neural networks under cyber-attacks

This paper focuses on the reachable set estimation for synchronizing of complex-valued neural networks (CVNNs) using an event-triggered (ET) approach and cyber-attacks. The system parameters are set up using Markovian switching rules. The proposed controller effectively saves the communication resources for the designed CVNNs. The main objective of this paper is to find an ellipsoid that can contain the state trajectory of the system as small as possible in the presence of control. From a physics point of view, the system can be likened to a dynamic system subjected to external perturbations, where the goal is to contain the trajectory of the system's state within a bounded region, similar to confining particle motion in phase space. To achieve this objective, we propose a novel approach based on the reachable set technique, which allows us to obtain an ellipsoid that contains the state trajectory of the system while minimizing its size. Utilizing the standard Lyapunov-Krasovskii functional (LKF), integral inequality approaches, some sufficient stability formed in terms of linear matrix inequalities (LMIs) are derived for the synchronization of CVNNs under the ET scheme, which can be solved using MATLAB's YALMIP toolbox. These conditions ensure that the states of the CVNNs converge to zero and that the synchronization error is bounded. Finally, numerical simulation results are provided to demonstrate the practicality and effectiveness of the proposed theoretical results.