# Sampled-data Output Regulation of Unstable Well-posed Infinite-dimensional Systems with Constant Reference and Disturbance Signals

## TL;DR

This paper develops a method for designing finite-dimensional sampled-data controllers to achieve output regulation and disturbance rejection in unstable infinite-dimensional systems with constant signals, using Nevanlinna-Pick interpolation.

## Contribution

It introduces a sufficient condition for the existence of such controllers and proposes a design approach based on interpolation techniques, extending to systems with delays.

## Key findings

- Finite-dimensional controllers can achieve output regulation for unstable infinite-dimensional systems.
- The design method employs Nevanlinna-Pick interpolation with interior and boundary conditions.
- Applicable to systems with state and output delays.

## Abstract

We study the sample-data control problem of output tracking and disturbance rejection for unstable well-posed linear infinite-dimensional systems with constant reference and disturbance signals. We obtain a sufficient condition for the existence of finite-dimensional sampled-data controllers that are solutions of this control problem. To this end, we study the problem of output tracking and disturbance rejection for infinite-dimensional discrete-time systems and propose a design method of finite-dimensional controllers by using a solution of the Nevanlinna-Pick interpolation problem with both interior and boundary conditions. We apply our results to systems with state and output delays.