Article Journal of Vibration and Control 2020, Vol. 0(0) 1–14 © The Author(s) 2020 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/1077546319891693 journals.sagepub.com/home/jvc Robust sliding mode observer design for simultaneous fault reconstruction in perturbed Takagi-Sugeno fuzzy systems using non-quadratic stability analysis Samira Asadi 1 , Alireza Khayatian 1 , Maryam Dehghani 1 , Navid Vafamand 1  and Mohammad Hassan Khooban 2 Abstract Appearing faults in a practical system is dispensable, and if it is not compensated, it results in poor system performance or even dysfunction of the system. The fault detection has become a promising challenging issue to guarantee the safety and reliability of systems. In this paper, a novel fuzzy-based sliding mode observer for the simultaneous actuator and sensor fault reconstruction of nonlinear systems subjected to external disturbance is proposed. The proposed approach employs the Takagi-Sugeno fuzzy model, sliding mode observer and non-quadratic Lyapunov function. First, by filtering the system output, a fictitious system whose actuator faults are the original actuator and sensor faults is constructed. Then, by considering the H ∞ performance criteria, the effect of disturbance on the state estimations is minimized. It is proved that the estimations asymptotically converge to their actual values for non-perturbed systems. In the process of designing the observer gains, some transformation matrices are obtained by solving linear matrix inequalities. The proposed approach has some superiority over the existing methods. First, considering the non-quadratic Lyapunov function leads to relaxed results and good estimation performance. Second, using the sliding mode observer makes the proposed approach in- sensitive to the uncertainties and unknown inputs and determines the shape and size of the fault. Third, assuming the premise variables are immeasurable makes the presented approach more applicable. In conclusion, two practical systems are considered and simulation results illustrate the merits of the proposed approach in comparison with the recent methods from the fast and precise fault detection performance viewpoints. Keywords Takagi-Sugeno fuzzy system, actuator fault, sensor fault, non-quadratic Lyapunov function, robust fault reconstruction, sliding mode observer, linear matrix inequalities, H ∞ performance 1. Introduction In the last decades, fault-tolerant control (FTC) has become an important issue to guarantee the safety and reliability of several practical applications (Alwi and Edwards, 2008; Chen et al., 2015; He, 2018; Lin et al., 2018). The FTC methods can be categorized into passive and active ap- proaches (Shen et al., 2013). In the active fault-tolerant control (AFTC), information obtained from the fault de- tection and isolation (FDI) scheme is needed. So, the ro- bustness of most AFTC systems depends on the robustness of the FDI (Zhang and Jiang, 2006). Therefore, FDI has become an increasingly significant research issue in control systems for many years. The goal of the FDI scheme can be divided into two parts: fault detection (getting an alert when a fault happens) and fault isolation (determining the location of the fault). One well-known classification is model-based FDI and non-model-based FDI (Gharesi et al., 2018; Hwang et al., 2010; Zhang et al., 2013, 2017). Among various model-based FDI approaches, Observer-based FDI tech- nique is most well known and it has two main purposes: expressing a residual evaluation function in order to be compared with a predefined threshold such as unknown input observers (Soleymani et al., 2019) or estimating the 1 School of Electrical and Computer Engineering, Shiraz University, Iran 2 Department of Engineering, Aarhus University, Denmark Received: 1 July 2018; accepted: 4 September 2019 Corresponding author: Navid Vafamand, School of Electrical and Computer Engineering, Shiraz University, Zand Street, Shiraz, Iran Email: n.vafamand@shirazu.ac.ir