Avoiding observability singularities in output feedback bilinear systems

Lucas Brivadis (1) , Jean-Paul Gauthier (2, 3) , Ludovic Sacchelli (2) , Ulysse Serres (1)

1 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique
2 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
3 CDE - Contrôle et Diagnostic pour l’Environnement

Control-affine output systems generically present observability singularities, i.e. inputs that make the system unobservable. This proves to be a difficulty in the context of output feedback stabilization, where this issue is usually discarded by uniform observability assumptions for state feedback stabilizable systems. Focusing on state feedback stabilizable bilinear control systems with linear output, we use a transversality approach to provide perturbations of the stabilizing state feedback law, in order to make our system observable in any time even in the presence of singular inputs.

Mots clés: observability; output feedback; transversality theory; stabilization; Observability; Transversality theory; Output feedback; Stabilization

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

Lucas Brivadis, Jean-Paul Gauthier, Ludovic Sacchelli, Ulysse Serres. Avoiding observability singularities in output feedback bilinear systems. SIAM Journal on Control and Optimization, 2021, 59 (3), pp.1759-1780. ⟨10.1137/19M1272925⟩. ⟨hal-02172420v2⟩