International Journal of Control, Automation and Systems 16(X) (2018) 1-11 http://dx.doi.org/10.1007/s12555-017-0546-8 ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555 Adaptive Observer and Fault Tolerant Control for Takagi-Sugeno De- scriptor Nonlinear Systems with Sensor and Actuator Faults Dhouha Kharrat, Hamdi Gassara, Ahmed El Hajjaji*, and Mohamed Chaabane Abstract: This paper concerns the problem of state, fault estimation (FE) and Fault Tolerant Control (FTC) of Takagi-Sugeno (T-S) descriptor systems affected by sensor, actuator and external disturbances simultaneously. An Adaptive Fuzzy Observer is firstly proposed to achieve a simultaneous estimation of descriptor system states, actu- ator and sensor faults by using the H ∞ optimization technique. A FTC is secondly proposed to stabilize the faulty descriptor system. Based on Lyapunov method, stability analysis and design conditions of the resulting closed-loop system are formulated in a set of Linear Matrices Inequalities (LMIs). The adaptive fuzzy observer and the FTC are independently designed, in order to avoid the coupling problem. Accordingly, the observer and controller gains are computed separately by solving a set of LMIs and then used to estimate the unmeasured states, sensor and actuator faults at the same time. Finally, a truck-trailer system application is given to illustrate the validity of the proposed approach. Keywords: Adaptive fuzzy observer, T-S descriptor systems, Actuator/sensor faults estimation, FTC, LMI, Lya- punov functional. 1. INTRODUCTION An important number of industrial applications such as electrical power lines and manufacturing processes can have an undesirable behavior because of sensor, actuator and/or process faults or even external disturbances. Gen- erally speaking, to overcome component malfunctions and to maintain a certain level of safety, reliability and per- formance efficiency of a dynamic system, techniques and tools of fault detection and isolation (FDI), fault estima- tion (FE) and fault tolerant control (FTC) have been es- tablished (see [1–7]). FDI strategy is used to monitor whether a fault occurs and in which component it is occurred. However, it is generally difficult in practical systems to have the exact information of the size of faults from a FDI strategy only. Accordingly, considerable attention has been devoted to FE; it provides further accurate information of the fault, such as shape, size and duration (see [8–10] and references therein). Furthermore, FE plays an important role in FTC, which is developed to preserve overall system stability as well as acceptable performance. It possesses the ability to accom- modate component failures automatically. By using the Manuscript received September 6, 2017; revised November 23, 2017; accepted December 8, 2017. Recommended by Editor Jessie (Ju H.) Park. Dhouha Kharrat, Hamdi Gassara, and Ahmed El Hajjaji are with Modeling, Information, and Systems Laboratory, University of Pi- cardie Jules Verne, UFR of Sciences, 33 Rue St Leu Amiens 80000, France (e-mails: kharrat.dhouha@yahoo.fr, gassara.hamdi@yahoo.fr, hajjaji@u-picardie.fr). Dhouha Kharrat, Hamdi Gassara, and Mohamed Chaabane are with Laboratory of Sciences and Techniques of Automatic control & computer engineering, University of Sfax, ENIS PB 1173, 3038 Sfax, Tunisia (e-mails: kharrat.dhouha@yahoo.fr, gassara.hamdi@yahoo.fr, chaabane.ucpi@gmail.com). * Corresponding author. obtained fault information, an additional controller can be designed to compensate the faults. More precisely, FTC guarantees the stability of a closed-loop system even in the presence of component malfunctions. Besides main- taining stability properties, it could also keep desirable performances. FTC approach has been firstly adapted for linear sys- tems (see [1, 11] and references therein). However, most realistic engineering systems have nonlinear behaviors. It is well known that T-S fuzzy representation is a good way to approximate a large class of nonlinear dynamic sys- tems [12]. T-S fuzzy models are nonlinear systems rep- resented by a set of local linear models. By fuzzy blend- ing of the linear system representations the overall fuzzy model of the system is achieved, which greatly facilitates observer/controller synthesis for complex nonlinear sys- tems. One of the primary advantage is that it offers an effective and simple design strategy to represent a nonlin- ear system. In the literature, many important results have been reported in [13–15] and [16]. Consequently, many researchers have interested to FTC approach for T-S fuzzy systems (see [17–19]). In [20] for example, authors have extended the adaptive observer pro- posed in [21] to FTC of T-S fuzzy models. c ⃝ICROS, KIEE and Springer 2018