Finite-time synchronization control of coupled partial differential systems

In this paper, we consider the finite-time synchronization control of coupled partial differential systems (PDSs). First, we derive the coupled synchronization error dynamics and transform the finite-time synchronization problem into the finite-time stabilization problem. Then, we design the finite-time synchronization controller and obtain a sufficient condition to guarantee the finite-time synchronization under the controller, based on a finite-time stability lemma and Lyapunov-Krosaviskii functional method. The effect of spatial domain on the finite-time synchronization is also embodied in this sufficient condition. Finally, the numerical example is given to illustrate the effectiveness of the result obtained in this paper.