State and output feedback finite-time guaranteed cost control of linear itô stochastic systems

The problem of guaranteed cost control based on finite-time stability for stochastic system is first investigated in this paper. The motivation of solving this problem arises from an observation that finite/infinite-horizon guaranteed cost control does not consider the transient performance of the closed-loop system, but guaranteed cost control based on finite-time stability involves this practical requirement. In order to explain this problem explicitly, a concept of the stochastic finite-time guaranteed cost control is introduced, and then some new sufficient conditions for the existence of state and output feedback finite-time guaranteed cost controllers are derived, which guarantee finite-times to chastic stability of closed-loop systems and an upper bound of a quadratic cost function. Furthermore, this problem is reduced to a convex optimization problem with matrix inequality constraints and a new solving algorithm is given. Finally, an example is given to illustrate the effectiveness of the proposed method.