Backstepping Design of Robust State Feedback Regulators for Linear $2 \times 2$ Hyperbolic Systems

Abstract

This technical note deals with the robust output regulation problem for boundary controlled linear $2 \times 2$ hyperbolic systems. Thereby, the output to be controlled can be located at one of the boundaries or is a pointwise in-domain output. By utilizing the internal model principle, a state feedback regulator is determined for a finite-dimensional signal model describing the exogenous signals. This amounts to stabilizing a hyperbolic PDE-ODE cascade coupled at an intermediate point. For this, a systematic backstepping method is developed to determine the stabilizing state feedback controller. The solvability of the considered output regulation problem can easily be verified on the basis of the nominal plant transfer behaviour. For non-destabilizing model uncertainties the robustness of the achieved output regulation is verified. An uncertain hyperbolic system with an in-domain output illustrates the results of the technical note.