Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input

We solve the problem of stabilization of a class of linear first-order hyperbolic systems featuring n rightward convecting transport PDEs and one leftward convecting transport PDE. We design a controller, which requires a single control input applied on the leftward convecting PDE´s right boundary, and an observer, which employs a single sensor on the same PDE´s left boundary. We prove exponential stability of the origin of the resulting plant-observer-controller system in the spatial L²-sense.