Robust $H_\infty$ observer-based stabilization of disturbed uncertain fractional-order systems using a two-step procedure

Yassine Boukal (1, 2) , Michel Zasadzinski (1) , Mohamed Darouach (1) , Nour-Edine Radhy (2)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 Laboratoire de Physique des Matériaux, Micro-électronique, Automatique et Thermique

The main objective of this work is the problem of robust H-infinity observer-based stabilization for a class of linear Disturbed Uncertain Fractional-Order Systems (DU-FOS) by using H-infinity norm optimization. Based on the H∞-norm analysis for FOS, a new design methodology is established to stabilize a linear DU-FOS by using robust H-infinity Observer-Based Control (OBC). The existence conditions are derived, and by using the H∞-optimization technique, the stability of the estimation error and stabilization of the original system are given in an inequality condition, where all the observer matrices gains and the control law can be computed by solving a single inequality condition in two step. Finally, a simulation example is given to illustrate the validity of the results.

Mots clés: Fractional-order system; Observer-based control; H-infinity norm; H-infinity observer design

Domaines: Automatique / Robotique

Yassine Boukal, Michel Zasadzinski, Mohamed Darouach, Nour-Edine Radhy. Robust $H_\infty$ observer-based stabilization of disturbed uncertain fractional-order systems using a two-step procedure. Stefan Domek et Pawel Dwarak. Theoretical Developments and Applications of Non-Integer Order Systems, 357, Springer International Publishing, pp.167-180, 2015, Lecture Notes in Electrical Engineering, 978-3-319-23038-2. ⟨10.1007/978-3-319-23039-9_14⟩. ⟨hal-01242708⟩