Lp-norm boundedness conditions of stable Davidson-Cole filters

Rachid Malti (1) , Mathieu Chevrié (1) , Christophe Farges (1) , Jocelyn Sabatier (1)

1 IMS - Laboratoire de l'intégration, du matériau au système

This paper starts by investigating the boundedness conditions of the L2-norm of the impulse response of Davidson- Cole type fractional filters cascaded with pure fractional inte- grators. Then, it extends these boundedness conditions to the Lp-norms, with 1 ≤ p ≤ ∞. An illustrative example is then presented. It allows evaluating the integral squared error of a CRONE control loop and compares it to a classical proportional- derivative controller on a parameter varying system.

Mots clés: L2 -norm; Lp -norm; fractional models; Davidson-Cole filters; stability; boundedness conditions

Domaines: Automatique

Rachid Malti, Mathieu Chevrié, Christophe Farges, Jocelyn Sabatier. Lp-norm boundedness conditions of stable Davidson-Cole filters. 2014 International Conference on Fractional Differentiation and its Applications (ICFDA), Jun 2014, Catania, France. ⟨10.1109/ICFDA.2014.6967390⟩. ⟨hal-01709572⟩