Stabilization of Stochastic Markovian Jump Systems with Partially Unknown Transition Probabilities and Multiplicative Noise

We are concerned with the problems of stability and stabilization for stochastic Markovian jump systems subject to partially unknown transition probabilities andmultiplicative noise, including the continuous- and discrete-time cases. Sufficient conditions guaranteeing systems considered to be asymptotically stable in the mean square are presented in the form of LMIs. Furthermore, the desired state feedback controllers are designed. It is shown that, by introducing the free-weighing matrix method, the results we have obtained not only are less conservative than the existing ones but also can be regarded as extensions of the corresponding results of Markovian jump systems without noise. Numerical examples are finally provided to illustrate the effectiveness of the proposed theoretical results.