Asymptotical synchronization for a class of coupled time-delay partial differential systems via boundary control

The asymptotical synchronization for coupled delay partial differential systems (PDSs) with boundary control is considered in this paper. First, the synchronization error dynamics are introduced and we turn the asymptotical synchronization problem into the asymptotical stabilization problem. The boundary controller is also presented. Then, by employing Lyapunov functional method, under the given boundary controller, sufficient conditions are provided which guarantee the asymptotical synchronization for the coupled delay PDSs. These sufficient conditions are given by linear matrix inequalities (LMIs), which are easy to be solved by the developed standard algorithms. Both the cases of node delay and coupling delay are considered. Finally, numerical examples are given to illustrate the effectiveness of the proposed theoretical results.