Simultaneous stabilization of a family of delay differential systems by a dynamic state feedback. (English. Russian original) Zbl 1485.93453
Differ. Equ. 57, No. 11, 1495-1515 (2021); translation from Differ. Uravn. 57, No. 11, 1516-1535 (2021).
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.
Reviewer: Gen Qi Xu (Tianjin)
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93D40 | Finite-time stability |
| 93C23 | Control/observation systems governed by functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
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