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Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2005

Stabilization of time-delay systems with a controlled time-varying delay and applications

Résumé

We study the stability of a linear system with a pointwise, time-varying delay. We assume that the delay varies around a nominal value in a deterministic way and investigate the influence of this variation on stability. More precisely we are interested in characterizing situations where the time-varying delay system is stable, whereas the system with constant delay is unstable. Our approach consists of relating the stability properties of a system with a fast varying point-wise delay with these of a time-invariant system with a distributed delay. Then we can use frequency domain methods to analyze the problem and to derive stability criteria. The results are first illustrated with two theoretical examples. Then, we study a model of a variable speed rotating cutting tool. Based on the developed theory, we thereby provide both a theoretical explanation and a quantitative analysis tool for the beneficial effect of a variation of the machine speed on enhancing stability properties, which was reported in the literature.
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Dates et versions

hal-02294297 , version 1 (08-12-2019)

Identifiants

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Wim Michiels, Vincent van Assche, Silviu-Iulian Niculescu. Stabilization of time-delay systems with a controlled time-varying delay and applications. IEEE Transactions on Automatic Control, 2005, 50 (4), pp.493-504. ⟨10.1109/TAC.2005.844723⟩. ⟨hal-02294297⟩
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