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In this paper, the output regulation problem is addressed for a class of linear hyperbolic infinite-dimensional systems with spatially varying coefficients modelling a large class of convection-dominated transport reaction systems. In particular, distributed parameter systems with bounded input and unbounded output operators are considered. First, we demonstrate a general conclusion about the exponential stability of the considered system by relating the stability to the solution of an associated differential equation. Based on the assumption that the hyperbolic system satisfies the exponential stability conditions, the main manuscript contribution is the development of two novel finite-dimensional regulators, output and error feedback regulators, such that the controlled output of the plant tracks a reference signal generated by a known signal process (exosystem). In order to guarantee the feasibility of the proposed regulators, the solvability of the corresponding Sylvester equations is discussed and the solvability conditions are provided. Finally, simulations of output regulation of an axial dispersion reactor and a relevant numerical example illustrate the main results and performance of the proposed regulators synthesis. [ABSTRACT FROM AUTHOR]

This paper investigates the output regulation problem for a class of regular first-order hyperbolic partial differential equation (PDE) systems. A state feedback and an error feedback regulator are considered to force the output of the hyperbolic PDE plant to track a periodic reference trajectory generated by a neutrally stable exosystem. A new explanation is given to extend the results in the literature to solve the regulation problem associated with the first-order hyperbolic PDE systems. Moreover, in order to provide the closed-loop stability condition for the solvability of the regulator problems, the design of stabilising feedback gain and its dual problem design of stabilising output injection gain are considered in this paper. This paper develops an easy method to obtain an adjustable stabilising feedback gain and stabilising output injection gain with the aid of the operator Riccati equation. [ABSTRACT FROM AUTHOR]