Observer Design for Simultaneous State and Fault Estimation for a Class of Discrete-time Descriptor Linear Models

¹ Laboratory of High Energy Physics and Condensed Matter, Faculty of Science Hassan II University of Casablanca. B.P 5366, Maarif, Casablanca, Morocco
² ECPI, Department of Electrical Engineering, ENSEM Hassan II University of Casablanca. B.P 8118, Oasis, Casablanca Morocco

^* e-mail: kaoutar.ouarid@gmail.com
^** e-mail: a.elassoudi@ensem.ac.ma
^*** e-mail: jalal.soulami@gmail.com
^**** e-mail: h.elyaagoubi@ensem.ac.ma

Abstract

This paper investigates the problem of observer design for simultaneous states and faults estimation for a class of discrete-time descriptor linear models in presence of actuator and sensor faults. The idea of the present result is based on the second equivalent form of implicit model [1] which permits to separate the differential and algebraic equations in the considered singular model, and the use of an explicit augmented model structure. At that stage, an observer is built to estimate simultaneously the unknown states, the actuator faults, and the sensor faults. Next, the explicit structure of the augmented model is established. Then, an observer is built to estimate simultaneously the unknown states, the actuator faults, and the sensor faults. By using the Lyapunov approach, the convergence of the state estimation error of the augmented system is analyzed, and the observer’s gain matrix is achieved by solving only one linear matrix inequality (LMI). At long last, an illustrative model is given to show the performance and capability of the proposed strategy.