Perturbations of Admissibility, Exact Controllability, Exact Observability and Regularity

TL;DR

This paper investigates how key properties of linear systems in Banach spaces, such as controllability and observability, remain stable under certain regular perturbations, extending previous results with new generalizations and examples.

Contribution

It proves invariance of admissibility, controllability, observability, and regularity under regular perturbations of generators, generalizing earlier findings with boundary systems and examples.

Findings

Invariance of controllability and observability under perturbations

Extension of previous results to Banach space setting

Illustrative boundary system examples included

Abstract

This paper is concerned with the notions of admissibility, exact controllability, exact observability and regularity of linear systems in the Banach space setting. It is proved that admissible controllability, exact controllability, admissible observation, exact observability and regularity are invariant under some regular perturbations of the generators, such results are generalizations of some previous references. Moreover, the related boundary linear systems and some illustrative examples are presented.