Analysis and stabilization for networked linear hyperbolic systems of rationally dependent conservation laws

In this paper, for a networked linear hyperbolic partial differential equations (PDEs) system of conservation laws, the propagation periods of which are rationally dependent, with coupled boundary conditions, we propose a novel approach to analyze its controllability and observability. In addition, we propose a design method of a stabilizing controller, where a boundary-input with boundary-valued feedback is considered. First, we characterize the control properties, such as controllability of such a PDE system, in terms of the corresponding ones of a finite-dimensional discrete-time system defined on the boundaries of the PDE system, which is derived by fully exploiting the method of characteristics. Since the obtained discrete-time system is low-dimensional, its analysis is relatively easier. Next, we propose a design method of a stabilizing controller based on this discrete-time system. Finally, numerical simulations are presented to show that the proposed method is effective.