Extension of Popov Absolute Stability Criterion to Nonautonomous Systems with Delays

Abstract : This paper extends in a simple way the classical absolute stability Popov criterion to multivariable systems with delays and with time-varying memoryles- s nonlinearities subject to sector conditions. The proposed sufficient conditions are expressed in the frequency domain, a form well-suited for robustness issues, and lead to simple graphical interpretations for scalar systems. Apart from the usual conditions, the results assume basically a generalized sector condition on the derivative of the nonlinearities with respect to time. Results for local and global stability are given, the latter concerning in particular the linear time-varying ones. For rational transfers, the frequency conditions are equivalent to some easy-to-ch- eck Linear Matrix Inequalities: this leads to a tractable method of numerical resolution by approximation. As an illustration, a numerical example is provided.
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Rapport
[Research Report] RR-3625, INRIA. 1999
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https://hal.inria.fr/inria-00073052
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Soumis le : mercredi 24 mai 2006 - 11:42:23
Dernière modification le : vendredi 25 mai 2018 - 12:02:04
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:32:46

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Pierre-Alexandre Bliman. Extension of Popov Absolute Stability Criterion to Nonautonomous Systems with Delays. [Research Report] RR-3625, INRIA. 1999. 〈inria-00073052〉

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