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ENERGY OF FRACTIONAL ORDER TRANSFER FUNCTIONS
Rachid MALTI*, Olivier COIS+, Mohammed AOUN+, François LEVRON¤ and Alain OUSTALOUP+
* Intelligence de les Instrumentations et les Systèmes
IUT de Sénart-Fontainebleau - Université Paris 12
Avenue Pierre Point, 77127 Lieusaint, France
Tel: +33 (0) 1 64 13 51 83
Fax: +33 (0) 1 64 13 4503
malti@univ-paris12.fr
+ Laboratoire d’Automatique et de Productique UMR 5131
Université Bordeaux I - ENSEIRB
351 cours de la Libération, 33405 Talence cedex, France
Tel: +33 (0) 556 842 418
Fax: +33 (0) 556 846 644
{cois, aoun, oustaloup}@lap.u-bordeaux.fr
¤ Institut de Mathématique de Bordeaux
Université de Bordeaux I
351 cours de la Libération, 33405 Talence cedex, France
levron@math.u-bordeaux.fr
The objective of the paper is to compute the impulse response energy of a fractional order transfer function having a single mode. The differentiation order n, defined in the sense of Riemann-Liouville, is allowed to be a strictly positive real number. A necessary and sufficient condition is established on n, in order for the impulse response to belong to the Lebesgue space L2 of square integrable functions on the positive axis.
Keywords: fractional order differentiation, impulse response energy, transfer function, dynamical system, fractional calculus
Session slot T-Th-M21: Posters of Design Methods and Optimal Control/Area code 2b : Linear Systems
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