Fault Detection for Uncertain Polynomial Fuzzy Systems Using H∞$$ {H}_{\infty } $$ Filter Design and Zonotopic Analysis

ABSTRACT This article proposes a new fault detection approach for polynomial fuzzy systems with parametric uncertainties using filter design and zonotopic analysis. First, a polynomial fuzzy filter that is robust against uncertainties is designed by solving a set of sum‐of‐square constraints. Second, zonotopic analysis of residual is presented to obtain the guaranteed adaptive residual thresholds. After that, zonotopic residual evaluation schemes, including zonotope‐based and interval‐based evaluation schemes, are presented to achieve fault detection. Then, a numerical simulation is presented, which shows that the proposed fault detection approach can improve the performance of fault detection compared with the existing ellipsoid‐based method. Finally, we apply the method to a tunnel diode circuit system to validate the effectiveness of the presented polynomial fuzzy approach.