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H2-norm of fractional transfer functions of implicit type of the first kind

Mathieu Chevrié 1 Rachid Malti 2 Christophe Farges 3 Jocelyn Sabatier 4
1 Automatique / CRONE
PSA - PSA Peugeot - Citroën, IMS - Laboratoire de l'intégration, du matériau au système
2 Automatique / CRONE
IMS - Laboratoire de l'intégration, du matériau au système
4 CRONE
IMS - Laboratoire de l'intégration, du matériau au système
Abstract : This paper studies the H2-norm, or impulse response energy, of fractional transfer functions of implicit type. The analytical expression of the H2-norm is first derived for an elementary fractional transfer function of the first kind with a single real pole. Series connection of such a transfer function with a pure fractional integrator and with another implicit transfer function of the first kind are then studied. Results developed in the paper are finally used to derive a criterion to evaluate the quality of an integer order approximation for an implicit type fractional order model of the first kind.
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https://hal.archives-ouvertes.fr/hal-01063022
Contributor : Christophe Farges <>
Submitted on : Thursday, September 11, 2014 - 11:05:05 AM
Last modification on : Tuesday, March 31, 2020 - 2:12:19 PM

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Mathieu Chevrié, Rachid Malti, Christophe Farges, Jocelyn Sabatier. H2-norm of fractional transfer functions of implicit type of the first kind. 19th IFAC World Congress, Aug 2014, Cape Town, South Africa. pp.2022-2027, ⟨10.3182/20140824-6-ZA-1003.01458⟩. ⟨hal-01063022⟩

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