Sensor fault and state estimation for uncertain fuzzy descriptor systems: An LMI approach

This paper deals with the problem of robust sensor fault diagnosis of Takagi–Sugeno fuzzy uncertain descriptor systems affected by bounded external disturbance with unmeasurable premise variables. This problem is solved using a descriptor approach to easily convert the stability conditions into linear matrix inequalities). By augmenting the sensor fault into a state vector, a fuzzy descriptor observer is constructed to simultaneously estimate the state and sensor faults and attenuate the effect of both modelling uncertainties and external disturbance on the estimation error. The faults affecting the system behaviour are considered as an auxiliary state variable. Based on the Lyapunov theory and L 2 technique, two different approaches are proposed to study the convergence of the state estimation error and the stability conditions are given in terms of linear matrix inequalities. Finally, an application to a model of rolling disk is given to show the applicability of the proposed approaches.