Stability and Stabilization for Discrete-time Markovian Jump Stochastic Systems with Piecewise Homogeneous Transition Probabilities

In this paper, the stability and stabilization problems for discrete-time Markovian jump stochastic systems with time-varying transition probabilities are investigated. The time-varying character of the transition probabilities is considered to be finite piecewise homogeneous and the variations in the finite set are considered to be a stochastic variation. First, a stability criterion is derived to guarantee the stochastic stability of the considered piecewise homogeneous Markovian jump stochastic system. Further, a sufficient condition on the existence of a mode-dependent state feedback controller is proposed such that the resulting closed-loop system is stochastically stable. In addition, the stability and stabilization problems are studied for the piecewise homogeneous Markovian jump stochastic system with incomplete transition descriptions. Finally, some simulation results are given to show the validity and potential of the developed results.