Dynamic event-triggering asynchronous dissipative control for discrete-time Markov jump singularly perturbed systems with hybrid cyber attacks

This paper addresses the issue regarding asynchronous dissipative controller for a type of discrete-time Markov jump singularly perturbed systems (MJSPSs) with hybrid cyber attacks. To further alleviate the transmission burden on the communication network, dynamic event-triggering rules are proposed. Considering the impact of both deception attacks and denial-of-service (DoS) attacks on the discussed discrete-time MJSPSs, a novel hybrid cyber attacks model is initially constructed to consolidate these two types of attacks. An asynchronous controller is well constructed considering the mode information of Markov chain is exceedingly hard to obtain. Consequently, a hidden Markov model (HMM) is proposed to formulate the asynchronous situation between modes of the original Markov chain and the constructed asynchronous controller. By constructing the Lyapunov-Krasovskii functional concerning the singular perturbation parameter (SPP), sufficient criteria of achieving stochastic stability with a specific dissipative performance for the closed-loop MJSPSs are secured. Subsequently, the design methodology of non-synchronous controller and the dynamic event-triggering rules are furnished in a systematical way. Eventually, the superiority of the proffered mechanism is demonstrated by an ameliorative DC motor mathematical model.