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Simultaneous fault reconstruction of TS fuzzy systems using robust sliding mode observer and non-quadratic stability analysis

This paper proposes a novel sliding mode observer (SMO) for disturbed Takagi-Sugeno (TS) fuzzy systems subject to simultaneous actuator and sensor faults. It is assumed that the premise variables of the TS fuzzy system are unmeasurable in general. By filtering the system output and introducing two changes of coordinates, the sensor and actuator faults and norm bounded disturbance estimations are guaranteed to converge asymptotically and simultaneously to their actual values. In addition, based on a non-quadratic Lyapunov function (NQLF), the transformation matrices associated with the changes of coordinates are designed by solving linear matrix inequalities (LMIs) constraints via the convex optimization techniques. Due to the usage of the NQLF, the proposed approach provides less conservative LMI conditions. Furthermore, since the premise variables are assumed to be unmeasurable, the presented method in this paper is applicable to a wide class of nonlinear systems represented by TS fuzzy models. Finally, practical one-link manipulator system is provided and numerical simulation is carried out to illustrate the effectiveness and the merits of the proposed SMO comparing with the existing results in the hand.