Hybrid-triggered scheme asynchronous control for hidden Markov jump systems with partially unknown probabilities and cyber attacks

This paper is concerned with the issue of hybrid-triggered scheme $H_{\infty }$ asynchronous control for networked Markov jump systems (MJSs) with probabilistic cyber attacks. First, in view of the subsistent phenomenon that the controller cannot capture the system modes synchronously, the hidden Markov model (HMM) with partly unknown probabilities is introduced in this article to describe such asynchronous phenomenon. In addition, the hybrid-triggered scheme includes time-triggered scheme and event-triggered scheme, in which the switching signal between two schemes obeys random Bernoulli distribution. By utilizing Lyapunov stability theory and matrix inequality technique, some sufficient conditions are developed, which can guarantee the networked MJSs mean-square asymptotically stable (MSAS) and $H_{\infty }$ performance; also, the desired controller gains are obtained by singular value decomposition (SVD) methods. Moreover, as the special cases of the results above, three corollaries are given. Finally, a numerical example and a pulse width-modulation-driven boost converter (PWMDBC) model are provided to demonstrate the usefulness and reliability of our developed approaches.