State and Fault Observer Design for a Class of Takagi-Sugeno Descriptor Models

Based on the singular value decomposition (SVD) approach, this paper deals with the problem of the fuzzy observer design in order to propose an actuator and sensor faults estimation method for a class of Takagi-Sugeno (T-S) descriptor models with measurable premise variables. More precisely, a new fuzzy observer design in explicit structure is developed to estimate simultaneously the system state and the unknown faults based on the use of an augmented fuzzy descriptor model which regroups the state variables, unknown faults and their successive derivatives. The exponential stability of the estimation error is studied by using the Lyapunov theory and the stability conditions are given in terms of linear matrix inequalities (LMIs). Finally, an application to a rolling disc process is given to illustrate the effectiveness of the proposed method.