On exact controllability of neutral type time-delay systems

TL;DR

This paper investigates the conditions under which neutral type time-delay systems can be exactly controlled, providing a criterion and identifying the critical time needed for controllability.

Contribution

It introduces a new controllability criterion for neutral time-delay systems using an operator model and eigenvector basis analysis.

Findings

Established a criterion for exact controllability

Identified the critical controllability time

Proposed feedback control modifications

Abstract

The paper is devoted to the problem of global exact controllability for a wide class of neutral and mixed time-delay systems. We consider an equivalent operator model in Hilbert space and formulate steering conditions of controllable states as a vector moment problem. The existence of a basis of eigenvectors of system operator allows to simplify substantially the form of the moment problem. A change of control by a feedback law allows to modify the system structure to guarantee the existence of a basis of eigenvectors of the corresponding operator. We prove a criterion of exact controllability and ascertain the precise critical time of controllability.