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On stability of commensurate fractional order systems

Jocelyn Sabatier 1, * Christophe Farges 1
* Corresponding author
IMS - Laboratoire de l'intégration, du matériau au système
Abstract : This paper proposes a new proof of the Matignon's stability theorem. This theorem is the starting point of numerous results in the field of fractional order systems. However, in the original work, its proof is limited to a fractional order nu such that 0 < nu < 1. Moreover, it relies on Caputo's definition for fractional differentiation and the study of system trajectories for non-null initial conditions which is now questionable in regard of recent works. The new proof proposed here is based on a closed loop realization and the application of the Nyquist theorem. It does not rely on a peculiar definition of fractional differentiation and is valid for orders nu such that 1 < nu < 2.
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Contributor : Christophe Farges <>
Submitted on : Monday, February 11, 2013 - 4:12:35 PM
Last modification on : Tuesday, October 15, 2019 - 12:30:05 PM



Jocelyn Sabatier, Christophe Farges. On stability of commensurate fractional order systems. International journal of bifurcation and chaos in applied sciences and engineering , World Scientific Publishing, 2012, 22 (4), pp.1-8. ⟨10.1142/S0218127412500848⟩. ⟨hal-00787246⟩



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