Stochastic stability and stabilization of discrete-time Markovian jump systems in the presence of incomplete knowledge of transition probabilities

This paper is concerned with the stability analysis and controller design for a class of discrete-time Markovian jump systems subject to incomplete knowledge of transition probabilities. Different from the previous results, some free-weighting matrices are introduced to obtain some new criteria with less conservatism. It is theoretically shown that the previous results are special cases if the free-weighting matrices are chosen to be some special forms. This brings much less conservatism compared with the previous ones. A numerical example is provided to show the effectiveness the proposed method.