Event-Triggered Global Finite-Time Sliding Mode Control for Impulsive Nonlinear Systems and Its Application to Coupled RDNNs

This article presents a novel event-triggered sliding-mode control (ET-SMC) strategy for impulsive nonlinear systems (INS) in the presence of matched disturbances. Most of the existing sliding mode control (SMC) strategies work well when the system continually converges toward a predefined sliding surface, but have been proven to be inapplicable for discontinuous systems subjected to impulsive disturbances. Consequently, it becomes crucial and imperative to develop SMC strategies tailored for discontinuous dynamics affected by impulsive phenomena. Leveraging the event-triggering mechanism with a time-varying threshold and incorporating piecewise Lyapunov function techniques, we propose a novel ET-SMC strategy. It is proved that the proposed control strategy can effectively avoid Zeno behavior and ensure the finite-time stability (FTS) of the considered system via finite-time control theory and innovative impulsive estimation schemes. Furthermore, our results quantitatively measure changes in convergence rate under varying impulsive conditions, which provides valuable insights for performance analysis and the design of SMC strategies in such scenarios. As a specific application, we apply the proposed ET-SMC strategy to coupled reaction-diffusion neural networks (RDNNs) in the presence of both cyber-attacks and matched disturbances. Finally, we present several simulation examples to illustrate the effectiveness and practical applicability of the analytical methods presented in this article.