One side invertibility for implicit hyperbolic systems with delays

TL;DR

This paper investigates the left invertibility of implicit hyperbolic systems with delays in infinite-dimensional spaces, establishing that invertibility is equivalent to that of a delay-free subsystem through a decomposition approach.

Contribution

It introduces a decomposition method that reduces the invertibility problem of delayed hyperbolic systems to a simpler delay-free subsystem analysis.

Findings

Invertibility of delayed systems is equivalent to that of a subsystem without delays.

Decomposition procedure simplifies the analysis of invertibility.

Results apply to systems in infinite-dimensional Hilbert spaces.

Abstract

This paper deals with left invertibility problem of implicit hyperbolic systems with delays in infinite dimensional Hilbert spaces. From a decomposition procedure, invertibility for this class of systems is shown to be equivalent to the left invertibility of a subsystem without delays.