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Time-delay systems with a controlled time-varying delay: stability analysis and applications

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3 Author(s)
Michiels, W. ; Dept. of Comput. Sci., Katholieke Univ., Leuven, Belgium ; Van Assche, V. ; Niculescu, S.-I.

We study the stability of a linear system with a point-wise, 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 example. 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.

Published in:

Decision and Control, 2004. CDC. 43rd IEEE Conference on  (Volume:5 )

Date of Conference:

14-17 Dec. 2004