Robust predictive control via output feedback for Markov jump systems

For the discrete-time Markov jump system, when the states are not all measurable, we develop a robust modelpredictive control with output feedback for the system with polytopic uncertainty as well as bounded disturbance. The quasi-linear time-varying parameters of this system are known in values at the current time, but unknown in the future time. By using the linear matrix inequalities and the variable transformation, we convert the min-max robust predictive control problem for infinite horizon performance cost into the optimization problem with linear matrix inequality constraints. By solving this problem, we obtain the output feedback law for closed-loop system. Under the conditions for the input and output, the closed-loop system is stochastically stable in the sense of quadratic boundedness as we defined. Finally, a numerical example is provided to illustrate the effectiveness of the controller.