State and Fault Interval Estimation for Discrete-Time Takagi–Sugeno Fuzzy Systems via Intermediate Observer Base on Zonotopic Analysis

Abstract

In this article, we study state and fault interval estimation method for discrete-time Takagi–Sugeno fuzzy systems. First, a novel intermediate observer via T-N-L structure with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance is designed. The intermediate observer proposed is designed with a higher degree of freedom due to the introduction of two auxiliary variables. Second, based on this novel intermediate observer, zonotopic analysis is utilized to give a range of the effects of unknown inputs and fault derivatives on state and fault estimation, thus interval estimation results for state and fault are obtained. The effectiveness of the proposed method is verified by a dc motor-controlled inverted pendulum system.