IFAC PapersOnLine 51-24 (2018) 1179–1184 ScienceDirect ScienceDirect Available online at www.sciencedirect.com 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2018.09.702 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. 1. INTRODUCTION Fault Detection and Isolation (FDI) is a field of engineering which concerns the monitoring of a system, by identifying if a fault has occurred and by defining the type of fault and its location. Fault Diagnosis (FD) formalism has received more and more attention due to the increased demands for higher safety and reliability of dynamic systems Venkata- subramanian (2003). One of the main research topics is the model-based FD technics for nonlinear systems which is still in progress Garcia (1997). Linear Parameter Vary- ing (LPV) systems are considered as a class of nonlin- ear systems whose dynamics depend on exogenous time varying parameters. Typically, the parameter values are assumed to be confined into a prescribed set Rabaaoui (2018). LPV systems have recently attracted the attention of the FD research community because such models can be used efficiently to represent some nonlinear systems and allow to apply powerful linear tools to complex nonlin- ear systems Shamma (1992). This has motivated some researchers from the FDI community to develop model- based methods using LPV models Bokor (2002). Moreover, descriptor or singular systems, are mathemat- ical models with the property to integrate static and dynamical equations into the same model. This property improves the capacity by describing a large class of phys- ical systems. Descriptor systems have many important applications, e.g. aircraft modelling Masubuchi (2004), estimation parameters in distillation columns Aguilera (2013), observer design for waste-water treatment plants, analysis of electrical systems Duan (2010) and others. Nevertheless, few results on FD for Descriptor Linear Parameters Varying systems (D-LPV) have been reported Rodrigues (2014). So, the study of such problems is of both practical and theoretical importance. Amongst other, the concept of time-delays are encountered in various fields such as biology, physics, networks or even engineering systems Koenig (2004), Briat (2015). The time-delay systems are also referred to hereditary systems, systems with after-effects, systems with time- lag and infinite dimensional systems Hassanabadi (2016). Delay can occur in the system dynamics Karimi (2012), the control input or the system output Briat (2011). Irrespective of which part of the system is affected by delays, the evolution of a time-delay system depends both on the present state and also on its history. In general, this dependence can be represented by a functional differential equation. In particular, the differential equations are best suited to describe a time-delay system. In the last two decade, a lot of of results have thus been obtained concerning the stability, stabilizability and state feedback control for descriptor systems with time delay Fridman (2002), Jong (2002). Concerning observer and FD design, very few works have been devoted to D-LPV systems with time delay Hassanabadi (2016) and it re- mains an active research area. The main purpose of this paper is to address the problem of robust fault detection of delayed D-LPV systems in- cluding disturbances and actuator faults. This presented FD method is based on comparing the on-line real system behavior to the monitoring estimation with time delays obtains by an Adaptive Polytopic Observer (APO). Moreover, the APO studied in this paper can be consid- ered as an improvement of the classical UIO advised by Hassanabadi (2016), in the sense that the convergence of the state estimation error and fault estimation error are proved even for a nonconstant fault case. In the case of a significant discrepancy is detected between Keywords: LPV Descriptor Systems, Delayed Descriptor Systems, Adaptive Observer, Fault Diagnosis, Actuator Fault, LMI Abstract: This paper deals with the problem of Fault Diagnosis (FD) for Descriptor-Linear Parameter Varying (D-LPV) systems with time delay. This proposed FD algorithm is based on an Adaptive Polytopic Observer. The proposed observer is able to detect and estimate faults despite the presence of disturbance. The existence conditions for the proposed observer are formulated by Linear Matrix Inequalities (LMI) which can be solved efficiently. The effectiveness of the proposed approach is illustrated by a numerical example. * Laboratory of Advanced Systems at the Tunisia Polytechnic School, University of Carthage, Tunisia; (e-mail: hammmdihabib@yahoo.fr,chokri.mechmeche@esstt.rnu.tn,naceur.benhadj@ept.rnu.tn ** Automation and Process Engineering Laboratory, University of Lyon, Lyon, F-69003, France; University of Lyon 1,CNRS UMR 5007, Villeurbanne, F-69622, France; e-mail: mickael.rodrigues@univ-lyon1.fr H. HAMDI * , M. RODRIGUES ** , C. MECHMECHE * and N. BENHADJ BRAIEK * Observer-based Fault Diagnosis for Time-Delay LPV Descriptor Systems