Event-triggered ℒ2 − ℒ∞ control for discrete-time Markov jump systems with DoS attacks and exogenous disturbance

This paper is concerned with the event-triggered $ \mathcal {L}_2-\mathcal {L}_\infty $ L2−L∞ control problem for discrete-time Markov jump systems with DoS attacks and exogenous disturbance. Instead of one common event-triggering scheme, multiple triggering schemes are introduced to sample system signals and the event-triggered Markov closed-loop jump systems are further obtained under the full state feedback controller. Generally, mode information of subsystems is not completely available for the modules of trigger and controller such that asynchronous jump behaviour may occur among the modes of subsystems, triggering scheme and controller. Thus, a hidden Markov model (HMM) is developed to describe such asynchronous behaviour. Meanwhile, security issues of networks are widely studied in recent many literature. For discrete-time Markov jump systems, few works consider cyber attacks, especially periodic Denial-of-Service (DoS) attacks. Based on the HMM, the DoS attacks are taken into account and a set of sufficient conditions are further presented to guarantee the $ \mathcal {L}_2-\mathcal {L}_\infty $ L2−L∞ control performance of the resulting Markov closed-loop jump systems. Subsequently, the design of controller and event-triggering parameters are provided by using matrix inequality method. Finally, an example is given to show the effectiveness of the proposed approach.