New Conditions for the Finite-Time Stability of Stochastic Linear Time-Varying Systems

In this paper we investigate the stochastic finitetime stability (SFTS) problem for linear time-varying systems. The system under consideration is described by an Ito type differential equation and the Ito differentiation rule is exploited to derive conditions for SFTS. The main contribution of the paper is that we use an approach based on time-varying quadratic Lyapunov functions, which allow us to obtain less conservative conditions than the time-invariant Lyapunov functions commonly used in the literature. More specifically, we obtain a sufficient condition based on the solution of a generalized Lyapunov differential equation (GLDE) and a sufficient condition requiring the solution of a feasibility problem involving a differential LMIs (DLMI) constraint. We shall show that the DLMI based condition is less conservative and is useful to develop a sufficient condition for stochastic finite-time stabilizability via state feedback; on the other hand the GLDE condition is more efficient from the computational point of view.