Fault Estimation for Polynomial Fuzzy Systems with Unmeasurable Premise Variables and Its Application to Bridge Crane System

This paper studies the fault estimation problem for polynomial fuzzy systems with unmeasurable premise variables. Considering the limitations of existing methods that require the convergence of the original system, a novel augmentedstate observer is proposed for polynomial fuzzy systems. Unlike compensation-vector-based approaches, the proposed method addresses the singularity problem and eliminates the traditional linear growth assumptions on unmeasurable premise variables, while only existence of the corresponding upper bounds rather than knowledge of their specific values is assumed. Moreover, the proposed method enables fully mismatched design, thereby enhancing both design flexibility and computational efficiency. Finally, the effectiveness of the proposed method is demonstrated through a bridge crane system as a case study.