Volatile Event-Triggered Control for Stochastic Hybrid Networks Vulnerable to DoS Attacks

In this paper, the stability of stochastic complex networks with impulsive effects vulnerable to asynchronous DoS attacks is studied. The volatile event-triggered control (ETC) is advanced, featuring a control gain characterized by a sign-indefinite function that follows specific volatile patterns. Furthermore, the concept of average volatile gain under DoS attacks is proposed to quantify the volatile control gain. To address the challenges posed by volatile control gain and DoS attacks, a generalized differential inequality is proposed, resulting in a broader application of the main results. Using stochastic analysis techniques, graph-theoretic methodology, and the Lyapunov method, improved stability criteria are established. In particular, the joint potential unstable factors of impulsive effects and DoS attacks on stability are theoretically revealed. Stochastic hybrid networks that apply ETC can achieve stability under certain conditions if the magnitude of the impulsive effects and the frequency and duration of DoS attacks are sufficiently limited. Additionally, by incorporating the dwell time into ETC, the Zeno phenomenon can be avoided. Finally, a numerical example is provided to illustrate the validity of the obtained results.