Received: 28 February 2018 Revised: 11 October 2018 Accepted: 17 November 2018 DOI: 10.1002/asjc.2022 SPECIAL ISSUE Fault diagnosis based on sliding mode observer for LPV descriptor systems Habib Hamdi 1 Mickael Rodrigues 2 Chokri Mechmeche 1 Naceur Benhadj Braiek 1 1 Laboratory of Study and Control Automation of Process (LECAP), Polytechnic School of Tunisia, La Marsa, Tunisia 2 Laboratory Automation and Engineering Process (LAGEP), University Lyon, CNRS UMR 5007, Lyon, France Correspondence Habib Hamdi, Laboratory of Study and Control Automation of Process (LECAP), Polytechnic School of Tunisia, La Marsa, Tunisia. Email: habibhemdi@gmail.com Abstract This paper considers the problem of fault detection and reconstruction of actu- ator faults for linear parameter varying descriptor systems. A polytopic sliding mode observer (PSMO) is constructed to achieve simultaneous reconstruction of LPV polytopic descriptor system states and actuator faults. Sufficient condi- tions for the existence and design algorithm of the proposed polytopic sliding mode observer are provided. In addition, the design of the PSMO is formulated in terms of linear matrix inequalities that can be suitably solved using convex optimization techniques. This PSMO can force the output estimation error to converge to zero in a finite time when the actuators faults are bounded through the reinjection of the output estimation error via a nonlinear switching term. The effectiveness of the design technique is illustrated through a simulation of an anaerobic bioreactor. KEYWORDS fault diagnosis, LPV descriptor systems, sliding mode observer 1 INTRODUCTION The fault detection and isolation (FDI) of faults in indus- trial systems is an important problem and has attracted lots of attention from researchers around the world during the past few decades. The detection and diagnosis of faults in a system are critical in avoiding abnormal event progression and reducing significantly the productivity loss. Research on FDI continues to progress using various approaches which range from unknown-input observers (UIO), pro- portional interal observers (PIO) [1] and adaptive poly- topic observers (APO) [2]. A switched LPV observer has been developed [3] in order to estimate the states and faults for discrete-time linear parameter varying (LPV) systems. In [4] a fault diagnosis method is developed for ordinary discrete polytopic linear parameter varying (LPV) systems. It consists of designing a global FDI scheme for estimating a sensor fault magnitude over a wide operating range applied to a winding machine. However, descriptor systems also known as singular systems, arise from a natural modeling process in charac- terizing a wide class of practical systems, including elec- tric, electronic, aircraft systems, and biological systems. Descriptor systems offer a powerful tool for system mod- elling since they allow the description of a system by both dynamic equations and algebraic constraints. Due to the universal existence of inherent nonlinearities in manufacturing processes, nonlinear singular systems and their applications should be specifically considered. On the other hand, it is well recognized that linear parameter varying (LPV) descriptor systems can approximate a highly complicated nonlinear singular system using the polytopic representation. The notion of this approach is to represent the descriptor system as an interpolation of simple local ............................................................................................................................................................... © 2019 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd Asian J Control. 2019;21:89–98. wileyonlinelibrary.com/journal/asjc 89