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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

7Modeling of FDEs and FDSs

7.1. Introduction

Chapters 13 were dedicated to the numerical simulation of FDEs using fractional integrators. As in the integer order case, the integration operator is the key tool for the modeling of FDSs. In Chapter 6, a theoretical framework was provided to the analysis of this operator. Moreover, it was proved that the Riemann–Liouville integration corresponds basically to a convolution process, obeying the well-known principles of the system theory [KAI 80].

This convolution interpretation provides a natural solution to the initialization of FDSs, recognized as a major problem of fractional calculus for a long time [LOR 01, FUK 04, TEN 14]. Numerical simulations highlight the role of the distributed state variable z(ω,t) in the interpretation of system transients and reciprocally the inability of pseudo-state variables x(t) to predict them [SAB 10a, TRI 09b, TAR 16a]. This type of modeling, based on fractional integrators, can be qualified as the closed-loop or internal representation [TRI 12b, TRI 12c].

Nevertheless, another representation of linear commensurate order fractional systems exists, which is not based on fractional integrators. The inverse Laplace transform of the elementary transfer function images provides another distributed model of this system, known as the diffusive representation [MON 98, HEL 98, MON 05a, MON 05b], which can be ...

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Publisher Resources

ISBN: 9781786302694Purchase Link