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Semi-linear diffusive representations for non-linear fractional differential systems

Audounet, Jacques and Matignon, Denis and Montseny, Gérard Semi-linear diffusive representations for non-linear fractional differential systems. (2001) In: Nonlinear control in the Year 2000. (Lecture Notes in Control and Information Sciences). Springer London, 73-82. ISBN 978-1-85233-363-8

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Official URL: http://dx.doi.org/10.1007/BFb0110208

Abstract

The stability of non-linear fractional differential equations is studied. A sufficient stability condition on the non-linearity is given for the input-output stability, thanks to many different reformulations of the system using diffusive representations of dissipative pseudo-differential operators. The problem of asymptotic internal stability is analyzed by a more involved functional analytic method. Finally, a fractional version of the classical Hartman-Grobman theorem for hyperbolic dynamical systems of order 1 is conjectured and reformulated, based upon known necessary and sufficient stability conditions for linear fractional differential equations.

Item Type:Book Section
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole nationale supérieure des Télécommunications - ENST (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Other partners > Telecom ParisTech (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
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Deposited By: Denis Matignon
Deposited On:30 Sep 2016 13:11

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