A Novel Approach to State and Unknown Input Estimation for Takagi–Sugeno Fuzzy Models With Applications to Fault Detection

In this paper, a novel approach is proposed for state and unknown input estimation of Takagi-Sugeno fuzzy systems. By introducing an augmented state vector, containing both system state and the unknown input, a functional observer is proposed to estimate this vector, and the proposed observer provides a highly flexible estimation output. Through casting the observer design problem into an equivalent solvability problem of a linear matrix equation with respect to the observer gains, the existence condition for the proposed observer is explicitly derived in terms of matrix rank. Furthermore, a parameterization methodology of the observer gain matrices is provided as well, which avoids directly solving the Sylvester equation. The proposed observer design scheme is further applied to the H_H
_∞
fault detection problem, and the effectiveness of the proposed approach is demonstrated by state and unknown input estimation for a tunnel diode circuit and fault detection for a continuously stirred tank reactor system.