Impulsive Control Under Event-Triggered Mechanism for Reaction-Diffusion Systems With Impulsive Disturbances

This study investigates the stability of reaction-diffusion systems (RDSs) under impulsive disturbances using an event-triggered impulsive control method. Our key contribution is providing Zeno-free conditions for the event-triggered mechanism (ETM), which is crucial due to the potential for impulsive disturbances to trigger the sampling threshold earlier than expected, leading to Zeno behavior. We address this challenge by deriving conditions that ensure the ETM operates without Zeno behavior, essential for practical control implementation. We further derive several sufficient conditions for the asymptotic stability of RDSs based on impulsive control theory. Special cases with specific disturbance rules are also discussed, offering a broader understanding of system stability under various conditions. To demonstrate the applicability of our theoretical findings, we apply our control strategies to an atmospheric pollution model. A numerical example is provided to validate the effectiveness of our approach and to offer theoretical guidance for real-world environmental pollution control.