This paper presents the design of a  ∞ sliding mode and an unknown input observer for Takagi-Sugeno (TS) systems. Contrary to the common approaches reported in the literature, which considers exact premise variables, this work deals with the problem of inexact measurements of the premise variables. The proposed method is based on a  ∞ criteria to be robust to disturbances, sensor noise and uncertainty on the premise variables. The observer convergence and stability are established by considering a quadratic Lyapunov function, which relies on a set of Linear Matrix Inequalities. Then, a dedicated observer scheme is considered to detect and isolate sensor faults. Finally, the performance and applicability of the proposed approach are illustrated through numerical experiments on a nonlinear model that represents the lateral dynamics of an electric vehicle.

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This article proposes an approach for the estimation of states, actuator, and sensor faults in nonlinear systems represented by a polytopic linear parameter varying (LPV) system with inexact scheduling parameters. In the traditional LPV approaches, the scheduling variables are considered to be perfectly known.However, in practical applications, their measurement may contain precision and calibration errors or noise that can affect the performance of the diagnostic systems. Therefore, this work proposes the design of a proportional multiple-integral sliding mode observer for fault diagnosis (FD) that copes with LPV systems with inexact scheduling parameters. Due to the introduction of some nonlinear functions, the proposed observer is a nonlinear parameter varying system for which stability and robustness performance are formulated using the Lyapunov technique and a H ∞ performance criterion. It is shown that the design conditions boil down to a set of linear matrix inequalities whose solution allows computing the observer gain matrix along with the tunable parameters of the nonlinear functions. Results obtained using the simulator of an octocopter-type unmanned aerial vehicle are used to demonstrate the applicability and performance of the proposed FD scheme. K E Y W O R D Sfault diagnosis, linear matrix inequalities, nonlinear parameter varying systems, proportional multiple-integral sliding mode observer INTRODUCTIONModern control systems are prone to faults, which can damage the systems themselves or the environments in which they operate. For this reason, fault diagnosis (FD) algorithms become essential, since they enable fault-tolerant actions that minimize the effect of faults and improve the overall system's reliability and safety. An FD algorithm can be seen as a two-step process in which at first the fault is detected, that is, a Boolean logic value about the presence of a fault is provided, 8420