Finite-time stochastic stability and stabilization of linear Markovian jump systems

The problems of finite-time stochastic stability analysis and controller synthesis of linear Markovian jump systems are considered in this paper. By introducing the definition of finite-time stochastic stability, a sufficient condition is first proposed to ensure that the state of the system does not exceed a certain threshold in mean square sense during a specified time interval. It is shown that finding the possible solution can be transformed into the feasibility of some matrix inequality constraints. Based on this, the mode-dependent state feedback controllers are designed to realize the finite-time stochastic stability of the closed-loop systems. Finally, two numerical examples are presented to illustrate the results.