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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00804801
Contributor : Rachid Malti <>
Submitted on : Tuesday, March 26, 2013 - 12:50:24 PM
Last modification on : Tuesday, March 31, 2020 - 2:12:19 PM

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Rachid Malti, Magalie Thomassin. Differentiation similarities in fractional pseudo-state space representations and the subspace-based methods. Fractional Calculus and Applied Analysis, De Gruyter, 2013, 16 (1), pp.273-287. ⟨10.2478/s13540-013-0017-8⟩. ⟨hal-00804801⟩

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