Finite-Time Stability and Stabilization of Linear Stochastic Parabolic Distributed Parameter Systems

This paper investigates the problem of finite-time stability (FTS) and finite-time stabilization problem for a class of linear Itô-type stochastic parabolic distributed parameter systems. First, the concept of FTS and finite-time stabilization in mean square sense are proposed. Second, several sufficient conditions are given for the concerned systems to be finite-time stable by introducing a Lyapunov function and utilizing linear matrix inequalities (LMIs) technique. Moreover, the results of finite-time stabilization were also given. Finally, a numerical example is given to illustrate the effectiveness of our results.