Finite-time synchronization of coupled stochastic partial differential systems

In this paper, the finite-time synchronization of coupled stochastic partial differential systems (SPDSs) is investigated. First, we get the synchronization error dynamics, and the finite-time synchronization problem is transformed into the finite-time stabilization problem of synchronization error dynamics. By virtue of the finite-time stability lemma, using Lyapunov-Krasoviskii functional method and Itö formula, the controllers guaranteing the finite-time synchronization for SPDSs are designed, and a sufficient condition is obtained. The effect of the spatial domain on the finite-time synchronization also can be read off from this sufficient condition. Finally, an example is presented to illustrate the effectiveness of the controller.