Observability analysis by Poincaré normal forms

Latifa Boutat-Baddas (1) , Driss Boutat (2) , Jean-Pierre Barbot (3)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 LVR - Laboratoire Vision et Robotique
3 ALIEN - Algebra for Digital Identification and Estimation

This paper deals with quadratic equivalence, normal forms of observability, characteristic matrices and normal quadratic numbers for nonlinear Single-Input Single-Output (SISO) systems. We investigated both cases; nonlinear systems linearly observable and nonlinear systems with one linear unobservable mode. Particularly, the effect of the normal quadratic numbers on the observer design is pointed out. Finally, a faster observability analysis is proposed using characteristic matrices and normal quadratic numbers. Throughout the paper, academic examples as well as bio-reactor example highlight our purpose.

Mots clés: Observability; Poincaré's normal form; Observability singularity.; Observability singularity

Domaines: Automatique / Robotique

Latifa Boutat-Baddas, Driss Boutat, Jean-Pierre Barbot. Observability analysis by Poincaré normal forms. Mathematics of Control, Signals, and Systems, 2009, 21 (2), pp.147-170. ⟨10.1007/s00498-009-0040-9⟩. ⟨hal-00423424⟩