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The design of a synchronous controller for a network beam equation with structural time-varying and general perturbations is studied. An infinite dimensional observer is established to estimate the total disturbance which is composed of structural time-varying disturbance and unknown disturbance. Assuming that all networked partial differential equations (PDEs) are connected by communication graph, a feedback controller based on observer is proposed to solve the synchronization problem, which provides many new methods for the control of distributed systems in network space. The controller designed in this paper has three objectives: (1) asymptotically compensate structural term disturbance and general disturbance; (2) ensure the asymptotic convergence between each network state and the virtual leader state to track the virtual leader; and (3) the converged state errors are converged in the sense of synchronization. By using the analytical semigroup method, the well-posedness of the networked closed-loop system is proved. Three kinds of network beam equations with observer feedback control are simulated, and the simulation results show that this control method is effective for the synchronization of the network PDEs.

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