A discrete-time sliding window observer for markovian switching system

Abdelfettah Hocine (1) , Mohammed Chadli (2) , Didier Maquin (1) , José Ragot (1)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 CREA - Centre de Robotique, d'Electrotechnique et d'Automatique

In this paper, a fault detection method is developed for switching dynamic systems. These systems are represented by several linear models, each of them being associated to a particular operating mode. To finding the system operating mode the proposed method is based on mode probabilities and on a new structure of discrete-time observer with a sliding window measurements. This observer results from a combination of a Finite Memory Observer (FMO) and a Luenberger Observer. The stability condition of the observer is formulated in terms of linear matrix inequalities (LMI) using a quadratic Lyapunov function. The method also uses a priori knowledge information about the mode transition probabilities represented by a Markov chain. The proposed algorithm is of supervised nature where the faults to be detected are a priori indexed and modelled. In this work, the method is applied for the fault detection of a linear system characterized by a model of normal operating mode and several fault models. A comparison with the Generalized Pseudo-Bayesian method shows the validity and some advantages of the suggested method.

Keywords: State estimation; diagnosis; Markovian switching system; multiple model; Lyapunov function; LMI; sliding observer

Domains: Automatic

Abdelfettah Hocine, Mohammed Chadli, Didier Maquin, José Ragot. A discrete-time sliding window observer for markovian switching system. 45th IEEE Conference on Decision and Control, CDC06, Dec 2006, San Diego, United States. pp.2661-2666, ⟨10.1109/CDC.2006.377684⟩. ⟨hal-00121698⟩