Discrete mode observability analysis of switching structured linear systems with unknown input: A graphical approach

Mohamed Ghassane Kabadi (1) , Taha Boukhobza (1) , Frédéric Hamelin (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

Switching linear systems are described by a set of continuous state-space models together with conditions (switching law) that decide which model (mode) of this set is valid for the current continuous state. This article deals with the problem of the observability of discrete mode in which the switching law is assumed to be unknown. The formalization of the problem, based on a graph-theoretic approach, is to express sufficient conditions for generic observability of the discrete mode assuming only the knowledge of the system's structure. These conditions allow us to obtain criteria of sensor placement in order to recover the discrete mode observability using properties of the graph associated to the system. We obtain a sensor placement procedure based on classical and well-known graph theory algorithms, which have polynomial complexity orders.

Mots clés: discrete mode observability; state and input observability; switching structured linear systems; graph theory

Domaines: Automatique / Robotique

Mohamed Ghassane Kabadi, Taha Boukhobza, Frédéric Hamelin. Discrete mode observability analysis of switching structured linear systems with unknown input: A graphical approach. Conférence Méditerranéenne sur l'Ingénierie Sûre des Systèmes Complexes, MISC 2011, May 2011, Agadir, Morocco. pp.CDROM. ⟨hal-00651061⟩