Error feedback regulation problem for regular linear systems

This article is devoted to the error feedback regulation problem (EFRP) for linear distributed parameter systems. The plant, assumed to be a regular linear system, is driven by an exosystem via a disturbance signal. The exosystem has its spectrum in the imaginary axis and also generates the reference signal to be tracked. The EFRP is to design an exponentially stabilizing controller so that the tracking error decays to 0 in a some sense. The main result in this article is to characterize, under some suitable assumptions, controllers solving the EFRP using the solution of a certain Sylvester equation. We apply our results to a problem involving system modelled by partial differential equations. In this example we consider a one-dimensional dam-river system described by a diffusive-wave equation to model the dynamic behavior of the unsteady flow in a river for shallow water.