On Finite-Time Stochastic Stability and Stabilization of Markovian Jump Systems Subject to Partial Information on Transition Probabilities

Abstract

The problems of finite-time stochastic stability and stabilization for a class of linear Markovian jump systems subject to partial information on transition probabilities are considered in this paper. By introducing the concept of finite-time stochastic stability for linear Markovian jump systems, a new method is proposed to ensure that the state trajectory remains in a bounded region of the state space in mean square sense over a pre-specified finite-time interval. Based on this stability result, the finite-time stochastic stabilization criterion is then given. Finally, two numerical examples are shown to illustrate the effectiveness of the proposed method.