Design on dynamic event and self-triggered control for systems with Markov jumps and denial-of-service attacks

This paper investigates the dynamic event-triggered control and self-triggered control problems for discrete-time Markov jump systems subjected to aperiodic denial-of-service attacks. A hidden Markov model is employed to design an asynchronous controller that mitigates the discrepancies between the system modes and the controller modes. An iterative approach is developed to derive sufficient conditions that guarantee the stochastic stability of discrete-time Markov jump systems within the context of aperiodic denial-of-service attacks, utilizing a dynamic event-triggered mechanism. The gain matrices of the asynchronous controller and the dynamic event-triggered control mechanism are determined by solving a series of linear matrix inequalities. Furthermore, based on the dynamic event-triggered control strategy, a self-triggered mechanism is developed to predict the next sampling time using current system information, thereby eliminating the need for continuous real-time evaluation of triggering conditions.