Robust Control Analysis With Model Transformation for Interval Type-2 Fuzzy Systems

Abstract

To address the problem of robust stability analysis for interval type-2 fuzzy systems (IT2FSs), this article proposes an innovative analysis approach based on model transformation. First, a classical piecewise linear approximation method is utilized to process the upper boundary membership functions and lower boundary membership functions of the footprint of uncertainty in IT2FSs, resulting in linear boundary membership functions (MFs) that are more convenient for analysis, along with the corresponding approximation error functions. Subsequently, a novel error model transformation method is introduced to handle these error terms. By constructing new fuzzy rules and MFs, the boundary error terms are converted into a new fuzzy model, thereby incorporating more information about the error functions into the stability analysis. Based on this model, a robust stability condition in the form of linear matrix inequalities are derived, achieving improved robustness. Finally, the effectiveness of the proposed method is validated through simulations on real-world systems, and its superiority is demonstrated by comparison with existing methods.