On Notions of Detectability and Observers for Hybrid Systems

Pauline Bernard (1) , Ricardo Sanfelice (2)

1 CAS - Centre Automatique et Systèmes
2 UCSC - Jack Baskin School of Engineering

An asymptotic observer is a dynamical system taking as input the plant's output and producing asymp-totically an estimate of the plant's state. It is commonly known that for an observer to exist, the plant must be asymptotically detectable, namely the trajectories giving the same output must asymptotically converge to one another. But unlike continuous-time and discrete-time systems, those notions are not straightforward to define for a hybrid plant, since solutions do not share the same hybrid time domain. In this paper, we propose to define observers and detectability for hybrid systems together, in a way that ensures detectability remains necessary for the existence of an observer and such that standard definitions are recovered for continuous-time and discrete-time systems. We rely on the recent definition of hybrid systems with hybrid inputs and use jump reparametrizations to define convergence and equality of outputs.

Mots clés: observer; hybrid systems; impulsive systems

Domaines: Systèmes dynamiques [math.DS]; Automatique / Robotique

Pauline Bernard, Ricardo Sanfelice. On Notions of Detectability and Observers for Hybrid Systems. 2020. ⟨hal-02525637v1⟩