On stability of commensurate fractional order systems - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International journal of bifurcation and chaos in applied sciences and engineering Année : 2012

On stability of commensurate fractional order systems

Jocelyn Sabatier
  • Fonction : Auteur correspondant
  • PersonId : 846068

Connectez-vous pour contacter l'auteur
Christophe Farges
  • Fonction : Auteur
  • PersonId : 853866

Résumé

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.

Domaines

Automatique
Fichier non déposé

Dates et versions

hal-00787246 , version 1 (11-02-2013)

Identifiants

Citer

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

Altmetric

Partager

Gmail Facebook X LinkedIn More