Conditions of exact null controllability and the problem of complete stabilizability for time-delay systems

TL;DR

This paper investigates the relationship between exact null controllability and complete stabilizability in linear time-delay systems, establishing their equivalence under certain eigenvector conditions.

Contribution

It proves the equivalence of complete stabilizability and exact null controllability for a class of time-delay systems with complete eigenvector properties.

Findings

Proves the equivalence of controllability and stabilizability under specific conditions

Identifies key eigenvector properties necessary for the equivalence

Provides theoretical foundation for control design in time-delay systems

Abstract

For a class of linear time-delay control systems satisfying the property of completability of the generalized eigenvectors we prove that the problems of complete stabilizability and exact null controllability are equivalent.