Event-Based $H_\infty$ Control for Discrete-Time Fuzzy Markov Jump Systems Subject to DoS Attacks

This article is concerned with
$H_\infty$
control problem for discrete-time Takagi–Sugeno fuzzy Markov jump systems with event-triggering scheme (ETS) and denial-of-service (DoS) attacks. Aperiodic DoS attacks characterized by duration and frequency are introduced. In the light of DoS attacks and event-triggered fuzzy controller, the switched fuzzy Markov jump closed-loop system is established. Particularly, in order to address the issue of mismatched behavior between membership functions of fuzzy system and fuzzy controller, a novel ETS consisting of membership functions is developed. Then, with the help of multiple Lyapunov function method and iterative technique, some sufficient conditions are provided to ensure the
$H_\infty$
performance of the resulting closed-loop system. Subsequently, the explicit parameter design of controller and ETS is provided. Finally, an example is employed to verify the validity of the proposed theoretical method.