Static Output Feedback Control for Interval Type‐2 <scp>T‐S</scp> Fuzzy Systems Based on Fuzzy <scp>L</scp>yapunov Functions

Abstract

Abstract This study aims to design an interval type‐2 ( IT 2) fuzzy static output feedback controller to stabilize the IT 2 T akagi‐ S ugeno ( T‐S ) fuzzy system. Conservative results may be obtained when a common quadratic L yapunov function is utilized to investigate the stability of T‐S fuzzy systems. A fuzzy L yapunov function is employed in this study to analyze the stability of the IT 2 fuzzy closed‐loop system formed by the IT 2 T‐S fuzzy model and the IT 2 fuzzy static output feedback controller. Stability conditions in the form of linear matrix inequalities are derived. Several slack matrices are introduced to further reduce the conservativeness of stability analysis. The membership‐function shape‐dependent analysis approach is also employed to relax the stability results. The numerical examples illustrate the effectiveness of the proposed conditions.