Weak controllability of second order evolution systems and applications

TL;DR

This paper introduces a new concept called weak controllability for second order evolution systems, establishing its equivalence with a related weak observability inequality, and explores its applications.

Contribution

It defines the weak controllability notion and proves its equivalence to weak observability, extending controllability theory for distributed parameter systems.

Findings

Introduces weak controllability concept.

Establishes equivalence with weak observability.

Provides applications of the new controllability notion.

Abstract

Controllability and observability are important properties of a distributed paramater systems.The equivalence between the notion of exact observability and exact controllability holds in general. In this work, we define a new notion of controllability say weak which is related to some weak observability inequality and we give the equivalence between.