Static Output Feedback Control for Interval Type‐2 T‐S Fuzzy Systems Based on Fuzzy Lyapunov Functions

Abstract

This study aims to design an interval type-2 (IT2) fuzzy static output feedback controller to stabilize the IT2 Takagi-Sugeno (T-S) fuzzy system. Conservative results may be obtained when a common quadratic Lyapunov function is utilized to investigate the stability of T-S fuzzy systems. A fuzzy Lyapunov function is employed in this study to analyze the stability of the IT2 fuzzy closed-loop system formed by the IT2 T-S fuzzy model and the IT2 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.

NON‐PDC Observer‐Based T‐S Fuzzy Tracking Controller Design and its Application in CHAOS Control

“…To show the validity of the proposed observer-based T-S fuzzy tracker design method in the design of a tracking controller for the nonlinear chaotic disc, we employ the LMIs of Theorem 1 to the T-S fuzzy system (23). Using LMILAB [45] in MATLAB®, we solve the LMIs (39)-(46) for the system (23). Assuming |x i | < d i with d i = 10 (i = 1 , .…”

“…In this paper, we design a tracking T-S observer-based controller which forces the states of the T-S model (23) to converge asymptotically to the desired trajectory given in (6). It is easy to show that the dynamics of (6) can be represented by the following T-S model…”

Transient stability and voltage regulation in the framework of the interval type‐2 fuzzy model‐based control systems

“…In recent works, nonlinear systems subject to parameter uncertainties are represented by the IT2 T-S fuzzy models [1][2][3][4][5][6][7][8][9]. The IT2 T-S fuzzy models in [5][6][7][8] are mainly the IT2 T-S fuzzy model used in IT2 FMB control systems. In this work, the IT2 T-S fuzzy model presented in Ref.…”

“…The stability analysis of interval type-2 (IT2) FMB control systems subject to parameter uncertainties is an interesting research topic to explore. Many studies have focused on applying T2 T-S fuzzy logic systems in the modeling of uncertain systems, and many successful results have been reported [1][2][3][4][5][6][7][8][9]. The authors in Refs [1][2][3][4] investigated the stability analysis of discrete-time IT2 fuzzy a Correspondence to: Abbadi Amel.…”

“…To address this difficulty, Xiao et al [9,10] divided the whole domain of the IT2 membership functions into some subdomains; in this way, only finite situations need to be considered in the stability analysis. All these approaches [1][2][3][4][5][6][7][8][9][10] require several assumptions to be made about the membership functions in order to enable the derivation of stability conditions, which makes the approach very difficult and valid only in specific cases. Furthermore, no systematic method is established to determine the parameters of the required membership functions.…”