Complete and Finite-Time Stabilization of a Delay Differential System by Incomplete Output Feedback

Abstract

For a spectrally controllable and simultaneously spectrally observable linear time-invariant system with commensurable delays, we construct one-dimensional output feedback controls that ensure the complete stabilization of the closed-loop system (the complete damping of the original system and the asymptotic stability of the closed-loop system) by an integro-difference controller and the finite-time stabilization (the complete damping of the original system) by a differential-difference controller. The results are illustrated with an example.