BIBO Stability Analysis of TSK Fuzzy PI/PD Control Systems

Abstract

In this paper, we determine the sufficient conditions in which nonlinear feedback systems using Takagi-Sugeno-Kang (TSK) fuzzy PI/PD controllers become bounded-input bounded-output (BIBO) stable. To determine BIBO stability conditions, we apply the small-gain theorem to the systems. Compared to previous results, BIBO stability conditions in this study are determined for controllers that are developed using more relaxed input fuzzy sets. In addition, the procedures used to determine sufficient conditions are simple because region-based input-output relationship analysis is not required. Finally, the derived conditions are less conservative than those determined in previous studies. MATLAB simulations are performed to validate the results of this study.