Transient performance improvement of Takagi‐Sugeno fuzzy systems by modified non‐parallel distributed compensation controller

Abstract

AbstractThis paper addresses the transient performance of nonlinear systems described by Takagi‐Sugeno (TS) fuzzy models. To achieve this goal, a modified fuzzy controller and a non‐quadratic Lyapunov function (NQLF) are utilized. The fuzzy controller comprises an α‐delayed non‐parallel distributed compensation (non‐PDC) and a nonlinear modifying term. The α‐delayed non‐PDC assures the global stabilization of the TS fuzzy systems through the NQLF and linear matrix inequality (LMI) numerical technique. Moreover, the modifying term is used to enhance the transient performance. It is shown that the stability of the closed‐loop system is guaranteed by the α‐delayed non‐PDC and the performance is improved by the modifying term. Two different selections for the modifying term are presented and that they can increase the reaching time of the response and lead to the finite‐time convergence of the state to their equilibrium point is proven. Several numerical and practical systems, that is, a single‐link manipulator and a chaotic permanent magnet synchronous machine, are simulated to illustrate the advantages of the proposed approach. The obtained numerical results are compared with other state‐of‐the‐art methods.