A Novel Approach to State and Unknown Input Estimation for Takagi–Sugeno Fuzzy Models With Applications to Fault Detection
Dong Zhao, Hak‐Keung Lam, Yueyang Li, Steven X. Ding, Shuai Liu
Abstract
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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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.