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Analysis, Modeling and Stability of Fractional Order Differential Systems 1
book

Analysis, Modeling and Stability of Fractional Order Differential Systems 1

by Jean-Claude Trigeassou, Nezha Maamri
September 2019
Intermediate to advanced content levelIntermediate to advanced
316 pages
5h 39m
English
Wiley-ISTE
Content preview from Analysis, Modeling and Stability of Fractional Order Differential Systems 1

6The Distributed Model of the Fractional Integrator

6.1. Introduction

In Part 1, and more specifically in Chapters 1 and 2, the Riemann–Liouville integration was defined, with a particular focus on the fractional order integrator. This operator was synthesized according to a frequency approach. Moreover, thanks to a partial fraction expansion, a modal representation was introduced. This result was not straightforward, considering the classical form of the integrator impulse response:

However, an important question is related to the limit of this modal model when the number of terms is increased to infinity.

The answer to this question is provided by the frequency distributed model of the fractional integrator, as a result of the inverse Laplace transform of images. This model provides answers to fundamental questions, for example, on the relation between frequency and modal representations, the expression of the Riemann–Liouville integral at any initial instant t0 and more globally on the internal distributed state z(ω, t) of the integrator.

Fundamentally, it will be demonstrated that the Riemann–Liouville integral of any function v(t) is a convolution between the impulse response hn (t) and v(t) , i.e. this integral can be interpreted as the response of an infinite dimension ...

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Publisher Resources

ISBN: 9781786302694Purchase Link