Asymptotical synchronization of a class of driving-response PDE networks with time delay and spatially variable coefficients

This paper addresses the problem of asymptotical synchronization for a class of driving-response partial differential equations (PDE) networks with time delay and spatially variable coefficients, modeled by two linear coupled parabolic PDEs. The objective of this paper is to design a distributed state feedback controller such that the driving-response PDE network is asymptotical synchronization. Using Lyapunov´s direct method and the technique of integration by parts, the main result of this paper is presented in term of a spatial differential linear matrix inequality (SDLMI). Finally, numerical simulation illustrates the effectiveness of the proposed design methods.