Robust Output Regulation for Continuous-Time Periodic Systems

TL;DR

This paper develops four novel control strategies for robust output regulation in continuous-time periodic systems, extending to time-invariant systems, with applications demonstrated on harmonic oscillators and heat equations.

Contribution

Introduction of four new controllers for robust output regulation in periodic systems, including extensions to time-invariant systems, with practical examples.

Findings

Four different controllers for output tracking and disturbance rejection.

Controllers applicable to both periodic and time-invariant systems.

Validated effectiveness through two illustrative examples.

Abstract

We consider controller design for robust output tracking and disturbance rejection for continuous-time periodic linear systems with periodic reference and disturbance signals. As our main results we present four different controllers: A feedforward control law and a discrete-time dynamic error feedback controller for output tracking and disturbance rejection, a robust discrete-time feedback controller, and finally a discrete-time feedback controller that achieves approximate robust output tracking and disturbance rejection. The presented constructions are also new for time-invariant finite and infinite-dimensional systems. The results are illustrated with two examples: A periodically time-dependent system of harmonic oscillators and a nonautonomous two-dimensional heat equation with boundary disturbance.