Asynchronous H∞ control of Markov jump discrete-time systems with incomplete transition probability and unreliable links

In this study, an asynchronous H-infinity state feedback controller is devised for Markov jump discrete time systems (MJDTSs) with time-varying delay. "Asynchronous " means that the system switching mode theta(k), the controller mode theta(k) and the quantizer mode lambda(k) are different from each other. The first one is homogeneous and the last two are non-homogeneous. In particular, as a promotion of existing work, we firstly attempt to propose the transition probabilities (TPs) of the three Markov chains (MCs) are not completely known. In addition, the discrete time-varying delay and its infinitely distributed ones are considered. Moreover, according to the Lyapunov stability theory and stochastic process, it is established for the sufficient criterion to ensure the stochastic stability of resulting closed-loop MJDTSs with an H-infinity attenuation performance index. The feasibility and effectiveness of the proposed method are validated by three examples. (C) 2021 ISA. Published by Elsevier Ltd. All rights reserved.