State feedback output regulation for a boundary controlled linear 2 × 2 hyperbolic system

In this manuscript, the output regulation is addressed for a boundary controlled 2 × 2 system of first order linear hyperbolic PDEs subject to process and boundary input disturbances. Under the assumption that the structure of the exosystem is known, the full state feedback boundary control law is developed to achieve disturbances rejection and the reference signal tracking, simultaneously. In addition, the stability of the closed-loop system is ensured with the aid of the backstepping stabilization approach. Furthermore, the existence of the unique solution of the resulting regulator equations is proved, which is essential to the solvability of the output regulation problem. A simulation example is studied to demonstrate the performance of the proposed regulator.