Boundary control synthesis for hyperbolic systems: A singular perturbation approach

In this paper, we consider the problem of boundary control of a class of linear hyperbolic systems of conservation laws based on the singular perturbation method. The full hyperbolic system is written as two subsystems, namely the reduced system representing the slow dynamics and the boundary-layer system standing for the fast dynamics. By choosing the boundary conditions for the reduced system as zero, the slow dynamics is stabilized in finite time. The main result is illustrated with a design of boundary control for a linearized Saint-Venant-Exner system. The stabilization of the full system is achieved with different boundary conditions for the fast dynamics.