Finite-Time and Practical Stability of a Class of Stochastic Dynamical Systems

In practice, one is not only interested in qualitative characterizations provided by Lyapunov and Lagrange stability, but also in quantitative information concerning system behavior, including estimates of trajectory bounds over finite and infinite time intervals. This type of information has been ascertained in a systematic manner using the notions of finite-time stability and practical stability. In the present paper we generalize some of the existing finite-time stability and practical stability results for deterministic dynamical systems determined by ordinary differential equations to dynamical systems determined by an important class of stochastic differential equations. We consider two types of stability concepts: finite-time and practical stability in the mean and in the mean square. We demonstrate the applicability of our results by means of several examples.