Annular Finite-Time Stabilization of Stochastic Linear Time-Varying Systems

This paper tackles the problem of Finite-Time Stability (FTS) and stabilization for the class of linear time-varying stochastic systems. In particular, we consider the case when the domains, where the state trajectories are required to belong in a given bounded time interval, do not contain the origin of the state-space. This can be the case of several applications, where the state values cannot go below a given threshold. For this class of systems, we present some sufficient conditions for FTS and FT stabilization via state feedback. These conditions are expressed in terms of differential linear matrix inequalities, or in terms of generalized differential Lyapunov equations. Extensive numerical simulations show that the proposed sufficient conditions are much less conservative than other conditions previously proposed in the literature.