Exact null controllability, complete stabilizability and exact final observability: the case of neutral type systems

TL;DR

This paper investigates the conditions for exact null controllability, complete stabilizability, and final observability in neutral type systems within Hilbert spaces, extending classical results to unbounded feedback scenarios.

Contribution

It extends the characterization of controllability and stabilizability to cases with unbounded feedback in neutral type systems, and establishes duality results for observability.

Findings

Extended controllability and stabilizability criteria to unbounded feedback cases.

Established duality between stabilizability and observability.

Provided illustrative examples demonstrating theoretical results.

Abstract

For abstract linear systems in Hilbert spaces we revisit the problems of exact controllability and complete stabilizability (stabilizability with an arbitrary decay rate), the latter property is equivalent to exact null controllability. We extend this result to the case when the feedback is not bounded. This enables the characterization of exact null controllability and complete stabilizability for neutral type systems. By duality, we obtain a result about continuous final observability.Illustrative examples are given.