Event-triggered Dynamic Output Feedback Control of Positive Markov Jump Systems under Denial-of-Service Attacks

This paper studies the design of event-triggered dynamic output feedback controllers for continuous-time positive Markov jump systems subject to unknown periodic denial-of-service (DoS) attacks. First, the attack signal is given. According to the characteristics of DoS attacks, the event-triggered condition is divided into two parts: the form of 1-norm during the attacks sleep and the end time of the attacks. Then, according to the two states of the attacks, the systems are modeled as positive Markov jump systems with switching form, that is, the open-loop systems with attacks and the closed-loop systems without attacks. Next, the event-triggered dynamic output feedback controller is designed to ensure the positivity and stability of the systems. At the same time, it is proved that there is no Zeno phenomenon. All results in this paper are described by linear programming. Finally, the effectiveness and practicability of the results are illustrated by simulation.