Exponential synchronization for a class of complex spatio-temporal networks with space-varying coefficients

This paper addresses the problem of exponential synchronization for a class of complex spatio-temporal networks with space-varying coefficients, where the dynamics of nodes are described by coupled partial differential equations (PDEs). The goal of this research is to design distributed proportional-spatial derivative (P-sD) state feedback controllers to ensure exponential synchronization of the complex spatio-temporal network. Using Lyapunov׳s direct method, the problem of exponential synchronization of the complex spatio-temporal network is formulated as the feasibility problem of spatial differential linear matrix inequality (SDLMI) in space. The feasible solutions to this SDLMI in space can be approximately derived via the standard finite difference method and the linear matrix inequality (LMI) optimization technique. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed design method.