Robust Output Regulation for a Linear 2 × 2 Hyperbolic System

This paper is concerned with the problem of error feedback output regulation of a linear $2 \times 2$ hyperbolic system with external disturbances. Firstly, we consider the system without the disturbances and introduce a transformation to make the tracking error become the output of the new system. Then, we design the regulator by the backstepping method and prove the closed-loop system is exponentially stable by the Lyapunov function approach. Finally, we prove the system with disturbances can be regulated by applying the regulator we designed.