Simultaneous stabilization of a family of delay differential systems by a dynamic state feedback (Q2070465)

In this paper the stabilization issue of a differential equation with commensurate delays and 1-d scalar control input is studied by the state extension method. A dynamic state feedback controller is constructed in the form of a differential-difference that provides the closed-loop system with finite-time stabilization (complete damping of the original system in finite time). The original system is reducing to a system with finite spectrum. The outer loop of the controller is constructed that provides the closed-loop system with finite-time stabilization. If the system is spectrally controllable, the approach is feasible and can be extended to apply to the case of a family of differential equations, thereby solving the problem of simultaneous finite-time stabilization of such a family. The results are illustrated by examples.