State and Fault Observer Design for Discrete-time Takagi-Sugeno Descriptor Models

Abstract

In this paper, the aim consists to propose a new methodology of fuzzy observer design allowing the simultaneous state and fault estimation based on the singular value decomposition (SVD) approach. More precisely, the study concerns a class of discrete-time Takagi-Sugeno descriptor models (DTSDMs) with measurable premise variables in presence of actuator and sensor faults. First, an augmented fuzzy descriptor model which regroups the state variables, unknown actuator and sensor faults is given. Next, a new fuzzy observer design in explicit structure is proposed. The exponential stability of the state estimation error is studied by using the Lyapunov theory and the stability conditions are given in term of linear matrix inequalities (LMIs). Finally, numerical simulations using a DTSDM of rolling disc process are given to highlight the performance of the proposed method of state and fault fuzzy observer design.