Exact eigenvalue assignment of linear scalar systems with single delay using Lambert W function

TL;DR

This paper provides an exact analytical solution for eigenvalue assignment in linear scalar systems with a single delay using the Lambert W function, including controller design and input-delay systems, supported by numerical examples.

Contribution

It introduces a novel exact eigenvalue assignment method for delayed scalar systems using Lambert W function, extending to input-delay systems.

Findings

Exact eigenvalue assignment achieved analytically.

Design procedure for feedback controller established.

Numerical examples validate the method.

Abstract

Eigenvalue assignment problem of a linear scalar system with a single discrete delay is analytically and exactly solved. The existence condition of the desired eigenvalue is established when the current and delay states are present in the feedback loop. Design of the feedback controller is then followed. Furthermore, eigenvalue assignment for the input-delay system is also obtained as well. Numerical examples illustrate the procedure of assigning the desired eigenvalue.