On the structural properties of an efficient feedback law

TL;DR

This paper analyzes the structural properties of an efficient feedback law for stabilizing linear time-reversible systems, highlighting differences between control types and explaining observed decay rate phenomena.

Contribution

It provides new insights into the domain of the generator, compares distributed and boundary controls, and offers a novel proof of exponential decay.

Findings

Generated a group by the closed-loop operator

Differentiated between distributed and boundary control complexities

Explained higher decay rates observed in experiments

Abstract

We investigate some structural properties of an efficient feedback law that stabilize linear time-reversible systems with an arbitrarily large decay rate. After giving a short proof of the generation of a group by the closed-loop operator, we focus on the domain of the infinitesimal generator in order to illustrate the difference bewteen a distributed control and a boundary control, the latter being technically more complex. We also give a new proof of the exponential decay of the solutions and we provide an explanation of the higher decay rate observed in some experiments.