Stochastic stabilization of Markovian jump systems in the presence of partial unknown transition probabilities and actuator saturation

This paper deals with the controller design problem for Markovian jump systems subject to partial unknown transition probabilities and actuator saturation. Different from the previous results where complete knowledge on the transition probabilities is available, a new controller synthesis scheme is proposed as well as an estimate of the domain of attraction in mean square sense. A sufficient condition is first established to guarantee the stochastic stability of the closed-loop system. An optimization problem with LMI constraints is then formulated to determine the largest contractively invariant set in mean square sense. Finally, a numerical example is provided to show the effectiveness of our method.