Robust stabilization of uncertain descriptor fractional-order systems

Ibrahima N'Doye (1, 2) , Mohamed Darouach (1) , Michel Zasadzinski (1) , Nour-Edine Radhy (3)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 ARC - Automation Research Group
3 LMPGI - Laboratoire Mécanique, Productique et Génie Industriel

This paper presents sufficient conditions for the robust asymptotical stabilization of uncertain descriptor fractional-order systems with the fractional order α satisfying 0 < α < 2. The results are obtained in terms of linear matrix inequalities. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in the state matrix. A necessary and sufficient condition for the normalization of uncertain descriptor fractional-order systems is given via linear matrix inequality (LMI) formulation. The state feedback control to robustly stabilize such uncertain descriptor fractional-order systems with the fractional order α belonging to 0 < α < 2 is derived. Two numerical examples are given to demonstrate the applicability of the proposed approach.

Mots clés: Descriptor fractional-order system; Parameter uncertainty; State feedback control; Normalization; Robust stabilization; Linear matrix inequality (LMI)

Domaines: Automatique / Robotique

Ibrahima N'Doye, Mohamed Darouach, Michel Zasadzinski, Nour-Edine Radhy. Robust stabilization of uncertain descriptor fractional-order systems. Automatica, 2013, 49 (6), pp.1907-1913. ⟨10.1016/j.automatica.2013.02.066⟩. ⟨hal-00878431⟩