Exponential synchronization for a class of networked linear parabolic PDE systems via boundary control

This paper addresses the problem of exponential synchronization via boundary control for a class of networked linear spatiotemporal dynamical networks consisting of N identical nodes, in which the spatiotemporal behavior of the each node is described by parabolic partial differential equations (PDEs). The purpose of this paper is to design boundary controllers ensuring the exponential synchronization of the networked parabolic PDE system. To do this, Lyapunov´s direct method, the vector-valued Wirtinger´s inequality, and the technique of integration by parts are employed. A sufficient condition on the existence of the boundary controllers is developed in term of standard of linear matrix inequality (LMI). Finally, numerical simulation results on a numerical example are presented to illustrate the effectiveness of the proposed design method.