Switching scheme, equivalence, and analog validation of the alternative fractional variable-order derivative definition

Author

Sierociuk, Dominik ; Malesza, Wiktor ; Macias, Michal

Author_Institution

Inst. of Control & Ind. Electron., Warsaw Univ. of Technol., Warsaw, Poland

fYear

2013

fDate

10-13 Dec. 2013

Firstpage

3876

Lastpage

3881

Abstract

In this paper, an alternative definition of variable-order differ-integral is proposed, both in a difference equation and matrix form. The derivation and explanation of the identity between the alternative definition and the reductive-switching scheme of variable-order derivative is introduced. Based on the switching scheme, an analog realization of the proposed variable-order derivative definition is presented. Moreover, obtained experimental results of the analog realization are compared with the numerical results.

Keywords

difference equations; differential algebraic equations; equivalence classes; integral equations; matrix algebra; realisation theory; time-varying systems; analog realization; analog validation; difference equation; equivalence; fractional variable-order derivative definition; matrix form; reductive-switching scheme; variable-order differ-integral; Approximation methods; Fractional calculus; Impedance; Numerical models; Printed circuits; Switches; Time-domain analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on

Conference_Location

Firenze

ISSN

0743-1546

Print_ISBN

978-1-4673-5714-2

Type

conf

DOI

10.1109/CDC.2013.6760481

Filename

6760481