Robust error feedback output regulation of a 2 × 2 hyperbolic system

In this paper, we consider the robust error feedback output regulation problem for a linear 2×2 hyperbolic system with system uncertainties and disturbance signals. Using the backstepping method, the state feedback controller for the system without the system uncertainties and the external disturbance signals (nominal system) is designed. In terms of the measurable regulation error, an observer system is designed to recover the state of the nominal system, and an observer-based error feedback controller is obtained to solve the robust output regulation problem. Moreover, we prove that the controller is robust to the system uncertainties and the disturbance signals, and show that the state of the closed-loop system is bounded. The numerical simulations are presented to illustrate the effectiveness of the theoretical results.