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Fractional Calculus and Applied Analysis

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Volume 16, Issue 1


Differentiation similarities in fractional pseudo-state space representations and the subspace-based methods

Rachid Malti / Magalie Thomassin
Published Online: 2012-12-27 | DOI: https://doi.org/10.2478/s13540-013-0017-8


The paper starts by presenting a new concept of differentiation similarity transformations for commensurate pseudo-states-space representations. It is proven that a pseudo-state-space representation with a commensurate differentiation order ν and a dimension of the transition matrix n can be similar to a pseudo-state-space representation with a commensurate order ν/k and a dimension of the transition matrix kn, where k is an integer number. A direct consequence of the aforementioned concept in fractional subspace-based identification methods for MIMO systems is that an overestimated pseudo-state-space representation has multiple minimums at commensurate differentiation orders over the integral number k. This result is especially visible when deterministic input/output signals are considered and less visible in the stochastic case due to overestimation.

MSC: Primary 26A33; Secondary 93B30

Keywords: similarity transformation; fractional calculus; subspace method; pseudo-state-space representation; system identification

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About the article

Published Online: 2012-12-27

Published in Print: 2013-03-01

Citation Information: Fractional Calculus and Applied Analysis, Volume 16, Issue 1, Pages 273–287, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-013-0017-8.

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© 2013 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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