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Research Papers

Equivalence of History-Function Based and Infinite-Dimensional-State Initializations for Fractional-Order Operators

[+] Author and Article Information
Tom T. Hartley

University of Akron,
Akron, OH 44325-3904
e-mail: thartley@uakron.edu

Carl F. Lorenzo

NASA Glenn Research Center,
Cleveland, OH 44135
e-mail: Carl.F.Lorenzo@nasa.gov

Jean-Claude Trigeassou

University of Bordeaux 1,
Talence Cedex, 33405, France
e-mail: jean-claude.trigeassou@ims-bordeaux.fr

Nezha Maamri

LIAS ENSIP University of Poitiers,
Poitiers Cedex, 86000France
e-mail: nezha.maamri@univ-poitiers.fr

Contributed by the Design Engineering Division for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received October 1, 2012; final manuscript received February 1, 2013; published online June 10, 2013. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 8(4), 041014 (Jun 10, 2013) (7 pages) Paper No: CND-12-1164; doi: 10.1115/1.4023865 History: Received October 01, 2012; Revised February 01, 2013

Proper initialization of fractional-order operators has been an ongoing problem, particularly in the application of Laplace transforms with correct initialization terms. In the last few years, a history-function-based initialization along with its corresponding Laplace transform has been presented. Alternatively, an infinite-dimensional state-space representation along with its corresponding Laplace transform has also been presented. The purpose of this paper is to demonstrate that these two approaches to the initialization problem for fractional-order operators are equivalent and that the associated Laplace transforms yield the correct initialization terms and can be used in the solution of fractional-order differential equations.

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Grahic Jump Location
Fig. 1

History function and initialization function for a fractional operator and the system initialization response

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