Resilient asynchronous state feedback control for Markov jump systems with transition probabilities partly unknown

This paper studies designing resilient asynchronous H
_∞
state feedback controller for Markov jump systems with transition probabilities partly unknown. By Finsler's Lemma, and with the help of three matrices with special structure, the problem of inter connection between the Lyapunov matrices and the system matrices is solved. In order to make the theory have more practical value, this paper considers the transition probabilities as partly unknown. The controller designed in this paper improves the robustness of the systems and is able to work when the jump between the system modes and the controller modes is asynchronous, meanwhile makes sure the system has a prescribed H
_∞
performance index but also is stochastically stable.