Finite-time control of discrete-time stochastic systems

This paper is concerned with the finite-time control problems of discrete-time stochastic systems. Firstly, we provide the sufficient conditions for the system to be finite-time stochastically robustly stabilizable via a state feedback, which can be applied to problems with both non-zero initial conditions and unknown exogenous disturbances. Then we give the sufficient conditions for the system to be finite-time stochastically stabilizable via an output feedback. These conditions are eventually reduced to feasibility problems of linear matrix inequalities. Finally, some examples are presented to illustrate the proposed methodology.