A critical case for stability of equilibria of delay differential equations and the study of a model for an electrohydraulic servomechanism

A general theorem is proved on the stability of an equilibrium point of a nonlinear delay differential equation, in the critical case when zero is a simple root of the characteristic equation for linearized equation. It extends the classical theorem of Malkin from the case of ordinary differential e...

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Bibliographic Details
Published in:Systems & control letters 2020-08, Vol.142, p.104722, Article 104722
Main Authors: Halanay, A., Safta, C.A.
Format: Article
Language:English
Subjects:
Delay differential equations
Electrohydraulic servomechanism
Lyapunov–Krasovskii functional
Stability
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Summary:A general theorem is proved on the stability of an equilibrium point of a nonlinear delay differential equation, in the critical case when zero is a simple root of the characteristic equation for linearized equation. It extends the classical theorem of Malkin from the case of ordinary differential equations. An application to the case of a electrohydraulic governor with delay in control is given.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2020.104722