Output regulation for general linear heterodirectional hyperbolic systems with spatially-varying coefficients

This article presents a backstepping solution to the output regulation problem for general linear heterodirectional hyperbolic systems with spatially-varying coefficients. The disturbances can act at both boundaries, distributed in-domain or at the output to be controlled. The latter is defined at a boundary, distributed or pointwise in-domain and has not to be available for measurement. By utilizing backstepping coordinates it is shown that all design equations are explicitly solvable. This allows a simple determination of a state feedback regulator, that is implemented by a reference and a disturbance observer. Furthermore, an easy evaluation of the existence conditions for the resulting output feedback regulator is possible in terms of the plant transfer behaviour. In order to facilitate the parameterization of the regulator, the resulting closed-loop dynamics is directly related to the design parameters. The proposed backstepping-based design of the output feedback regulator is demonstrated for an unstable heterodirectional 4  × 4 hyperbolic system.