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Fractional Derivatives and Diffusive Representations: Semigroup formulation, Stability issues and Engineering Applications

Matignon, Denis Fractional Derivatives and Diffusive Representations: Semigroup formulation, Stability issues and Engineering Applications. (2017) In: Control of Distributed Parameter Systems (CDPS 2017), 3 July 2017 - 7 July 2017 (Bordeaux, France).

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Official URL: https://www.math.u-bordeaux.fr/~bhaak/control-distributed-parameter.pdf

Abstract

Viscoelastic materials are often characterized by a completely monotone kernel : this gives rise to dynamical systems involving a convolution term. These systems can be treated in a quite general framework, but still, an efficient way of tackling these convolution terms is to transform them into so-called diffusive representations. The idea is to add an extra memory variable to the original system, which helps suppress the convolution term : it amounts to a kind of a realization, in the sense of systems theory. In the linear case, the analysis of such an augmented system can be performed within the framework of evolution semigroups. Eventhough some Lyapunov functional is to be found for the augmented system, LaSalle’s invariance principle can not be applied to it, since a lack of compactness is to be found in the equivalent model : hence, for the proof of asymptotic stability property, we resort to Arendt-Batty theorem.

Item Type:Invited Conference
Audience (conference):International conference proceedings
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Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
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Deposited By: Denis Matignon
Deposited On:13 Jun 2018 11:22

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