Hybrid Observer-based Asymptotic Stabilization of Non-uniformly Observable Systems: a Case Study

Mohamed Maghenem (1) , William Pasillas-Lépine (2) , Antonio Loria (2) , Missie Aguado-Rojas (3)

1 GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics
2 L2S - Laboratoire des signaux et systèmes
3 Hitachi Astemo

We solve an open problem of output-feedback stabilization for a nonlinear system that is not uniformly observable at the target equilibrium. The plant's model is of interest not only because it is an instance of the well-studied class of bilinear non-uniformly observable systems, but also because it represents the dynamics of an antiblock-braking system (ABS). To stabilize the origin, where the system is unobservable, we use a switched observer previously reported and a novel hybrid controller. The former relies on making the system operate in a regime that induces enough excitation to ensure the state estimation, while the latter is based on tracking a vanishing piecewise-constant reference. Our main statement establishes asymptotic stability of the origin in a hybrid sense.

Mots clés: Non-uniformly observable systems; observers; hybrid control; ABS

Domaines: Automatique

Mohamed Maghenem, William Pasillas-Lépine, Antonio Loria, Missie Aguado-Rojas. Hybrid Observer-based Asymptotic Stabilization of Non-uniformly Observable Systems: a Case Study. IEEE Transactions on Automatic Control, In press, https://ieeexplore.ieee.org/document/10264115. ⟨10.1109/TAC.2023.3319161⟩. ⟨hal-03870029v2⟩