Observer synthesis for a class of Takagi–Sugeno descriptor system with unmeasurable premise variable. Application to fault diagnosis

This paper proposes a methodology to design a Takagi–Sugeno (TS) descriptor observer for a class of TS descriptor systems. Unlike the popular approach that considers measurable premise variables, this paper considers the premise variables depending on unmeasurable vectors, e.g. the system states. This consideration covers a large class of nonlinear systems and represents a real challenge for the observer synthesis. Sufficient conditions to guarantee robustness against the unmeasurable premise variables and asymptotic convergence of the TS descriptor observer are obtained based on the H∞ approach together with the Lyapunov method. As a result, the designing conditions are given in terms of linear matrix inequalities (LMIs). In addition, sensor fault detection and isolation are performed by means of a generalised observer bank. Two numerical experiments, an electrical circuit and a rolling disc system, are presented in order to illustrate the effectiveness of the proposed method.