Finite-time Contraction Stability of Linear Stochastic Parabolic Distributed Parameter Systems with Time-varying Delay

This paper deals with the problem of finite-time contraction stability (FTCS) for a linear stochastic parabolic distributed parameter system with time-varying delay. We construct a Lyapunov-Krasovskii (L-K) function and utilize linear matrix inequalities (LMIs) to give the sufficient conditions for FTCS of this system in mean-square sense. Furthermore, the state feedback controller is designed to achieve FTCS of the corresponding closed-loop system in mean-square sense according to the given sufficient conditions. Finally, a simulation example is given to verify the validity of the results.