Exact observability and controllability for linear neutral type systems

TL;DR

This paper investigates the exact observability and controllability of linear neutral type systems using an infinite dimensional approach, establishing duality relations and deriving conditions for observability.

Contribution

It introduces a novel infinite dimensional framework for analyzing observability and controllability in neutral type systems, highlighting the duality and providing explicit conditions.

Findings

Established duality between observability and controllability.

Derived explicit observability conditions for neutral type systems.

Linked initial system states with adjoint system representations.

Abstract

The problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach. The duality with the exact controllabil-ity problem is the main tool. It is based on an explicit expression of a neutral type system which corresponding to the abstract adjoint system. A nontrivial relation is obtained between the initial neutral system and the system obtained via the adjoint abstract state operator. The characterization of the duality between controllability and observability is deduced, and then observability conditions are obtained.