Reliable control for discrete-time Markovian jump systems with partly unknown transition probabilities

In this paper, the reliable control problem is studied for a class of discrete linear Markovian jump systems with actuator failures. A more practical model of actuator failures than outage is considered. It is important that the transition probabilities of the jumping process are assumed to be partly unknown. The failures of actuator are quantified by a variable taking values in a given interval. The purpose of the addressed reliable control problem is to design a reliable controller based on the state feedback method such that the closed-loop systems is asymptotically mean-square stable disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures. The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities(LMIs). A numerical example is provided to demonstrate the effectiveness of the proposed design approach.