Mean-Square Bounded Synchronization for Complex Networks Under Cyber-Attack via Hybrid Self-Triggered Impulsive Control

The issue of mean-square bounded synchronization for complex networks subject to random disturbances, time-varying delays, and cyber-attacks is investigated in this paper. We employ static and dynamic self-triggered impulsive control strategies, which can predict the next impulsive instant based on the current state of the system. These strategies not only ensure the convergence of the control error but also reduce the number of triggering instants. Denial-of-service (DoS) and deception attacks are jointly modeled using two independent Bernoulli stochastic processes. Meanwhile, sufficient conditions for the mean-square bounded synchronization are established through the Lyapunov functional method. In addition, it is demonstrated that these control strategies rule out Zeno behavior, ensuring the reliable achievement of mean-square bounded synchronization. Finally, the accuracy of the theoretical analysis is illustrated through numerical examples. Compared to static triggering, the dynamic self-triggered impulsive control mechanism demonstrates superior performance in reducing the number of triggers, as shown by experimental results.