A DISCRETE-TIME SLIDING WINDOW OBSERVER FOR MARKOVIAN SWITCHING SYSTEM: AN LMI APPROACH

Abstract

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 find the system in 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.