Event-triggered impulsive control for switched delay systems and its application in image encryption of switched neural networks.

This paper addresses the event-triggered impulsive control problem for nonlinear switched systems with time delay. The main challenge is that the delayed state may originate from a historical interval governed by a subsystem different from the current one, while switching may also occur before the next impulse is generated. To address this issue, a mode-dependent event-triggered mechanism is developed by incorporating an exponential attenuation term associated with the initial historical information. Based on the Lyapunov-Razumikhin method and the average dwell time technique, sufficient criteria are established to ensure exponential stability of the considered system and rule out Zeno behavior. An explicit lower bound on the inter-event times is also obtained, which characterizes the admissible triggering intervals under the combined influence of switching and delay. Since the impulse input is applied only at triggering instants, no continuous control signal needs to be transmitted between two successive triggers, and the communication burden associated with control transmission from the controller to the actuator can be reduced. The proposed theoretical results are further applied to the synchronization of switched neural networks, where the design conditions for the triggering mechanism and impulsive control gain are formulated as linear matrix inequalities. Numerical simulations and an image encryption application demonstrate the effectiveness and practical applicability of the developed method.