Robust State Feedback Regulator Design for General Linear Heterodirectional Hyperbolic Systems

The topic of this paper is the backstepping-based solution of the robust state feedback regulation problem for general linear heterodirectional hyperbolic systems with spatially varying coefficients. Thereby, a large class of outputs is considered, i.e., mixed distributed and pointwise in-domain or boundary outputs. The state feedback regulator design is based on the p-copy internal model principle. This results in a stabilization problem for a cascade of m + p boundary controlled transport partial differential equations (PDEs) with p ordinary differential equations (ODEs). For this, a systematic backstepping approach is presented, in which all design equations are explicitly solvable in backstepping coordinates. Furthermore, the solvability conditions for the considered output regulation problem can be evaluated in closed form utilizing the plant transfer behavior. Robust output regulation is verified for nondestabilizing model uncertainties and unknown disturbance input locations. A 4 × 4 hyperbolic system with uncertain transport velocities and couplings in the transport PDEs illustrates the results of this paper.