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Solution of Time-Variant Fractional Differential Equations With a Generalized Peano–Baker Series

Eckert, Marius; Nagatou, Kaori; Rey, Felix; Stark, Oliver; Hohmann, Soren

Abstract (englisch):
Time-variant fractional systems have many applications. For example, they can be used for system identification of lithium-ion batteries. However, the analytical solution of the time-variant fractional state space equation is missing so far. To overcome this limitation, the present paper introduces a novel matrix approach, namely the generalized Peano-Baker Series, which is comparable to the transition matrix in the case of ordinary systems. Using this matrix, the solution of the time-variant fractional state space equation is derived. The initialization process is taken into account, which has been proven to be a crucial part for fractional operator calculus. Following this initialization, a modified definition of a fractional state is presented.

DOI: 10.1109/LCSYS.2018.2852600
Zitationen: 1
Zugehörige Institution(en) am KIT Institut für Regelungs- und Steuerungssysteme (IRS)
Institut für Analysis (IANA)
Publikationstyp Zeitschriftenaufsatz
Jahr 2019
Sprache Englisch
Identifikator ISSN: 2475-1456
KITopen-ID: 1000084842
Erschienen in IEEE Control Systems Letters
Band 3
Heft 1
Seiten 79–84
Vorab online veröffentlicht am 03.07.2018
Schlagworte fractional, Peano-Baker Series, time-variant system, Riemann-Liouville, Caputo
Nachgewiesen in Scopus
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