Asymptotical Synchronization of Coupled Time-delay Partial Differential Systems via Pinning Control and Boundary Control

This paper focus on the asymptotic synchronization issue of coupled time-delay PDSs via pinning control and boundary control. The asymptotic synchronization of PDSs with both node-delay and coupling delay is discussed firstly. Then the pinning controller and boundary controller are also presented in order to achieve the asymptotic synchronization. Further more, synchronization criteria are established by using the Lyapunov function method and inequality techniques. Obviously, it is an efficient control technique to combine the pinning control with the boundary control for the asymptotic synchronization of the PDSs. Finally, an example of digital simulation is used to elucidate the practicability and validity of our control method and the correctness of the theorem.