A new robust D-stability condition for real convex polytopic uncertainty

Dimitri Peaucelle (1) , Denis Arzelier (2) , Olivier Bachelier (3) , Jacques Bernussou (3)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
3 LAAS - Laboratoire d'analyse et d'architecture des systèmes

The problem of robust D-stability analysis with respect to real convex polytopic uncertainties is tackled. A new LMI-based sufficient condition for the existence of parameter-dependent Lyapunov functions is proposed. This condition generalises previously published conditions. Numerical comparisons with quadratic stability results as well as previous results based on parameter dependent Lyapunov functions illustrate the relevance of this new condition. Finally, this result appears to be promising for robust multi-objective performance analysis and control synthesis purposes.

Mots clés: Robust stability; quadratic stability; parametric uncertainty; LMIs; parameter-dependent Lyapunov functions

Domaines: Automatique

Dimitri Peaucelle, Denis Arzelier, Olivier Bachelier, Jacques Bernussou. A new robust D-stability condition for real convex polytopic uncertainty. Systems and Control Letters, 2000, 40 (1), pp.21-30. ⟨10.1016/S0167-6911(99)00119-X⟩. ⟨hal-03310541⟩