Left-coprimeness condition for the reachability in finite time of pseudo-rational systems of order zero with an application to difference delay systems

TL;DR

This paper establishes conditions for finite-time reachability in pseudo-rational systems of order zero, providing bounds and characterizations that are applied to difference delay systems with distributed delays.

Contribution

It introduces a left-coprime condition that characterizes reachability in finite time for pseudo-rational systems of order zero, with practical applications to delay systems.

Findings

Derived a bound on minimal reachability time

Characterized reachability via a left-coprime condition

Applied results to difference delay systems with distributed delays

Abstract

The paper investigates the reachability in finite time of pseudo-rational systems of order zero. A bound on the minimal time of reachability is obtained and the reachability property for integrable functions is characterized in terms of a left-coprime condition. The results are applied to difference delay systems with distributed delays.