The Dependence of Stability upon Membership Functions in LMI-based Fuzzy Control

歸屬函數對於模糊控制系統穩定性之影響

10.6358/JCYU.200503.0103

練光祐(Kuang-Yow Lian)；杜慧雯(Hui-Wen Tu)；廖志傑(Jeih-Jang Liou)

T-S模糊模型 ； 線性矩陣不等式 ； 穩定條件 ； T-S fuzzy model ； LMI ； Stabilization

中原學報

33卷1期（2005 / 03 / 01）

103 - 110

英文

本論文中主旨在討論以線性矩陣不等式爲基礎的模糊控制器的穩定條件，特別針對模糊模型與控制器間具有不同的歸屬函數。文中我們分別利用Lypaunov方法和Kharitonov's理論去分析穩定條件，並且討論適應性模糊控制器的情況。

In this paper, we investigate the stability conditions for LMI-based fuzzy control design. Especially, we focus on the dependence of the stability upon membership functions. Applying Lyapunov equation and a convex hull of fuzzy subsystems, we first establish a nearly equivalent relationship of a stable interval characteristic polynomial and a set of feasible LMIs. Then Kharitonov's theorem gives a guideline for the solvability of stabilization problem using LMI-based design. On the other hand, the LMI condition leads to the well-known results for LMI-based fuzzy control design. We further indicate that the different LMI conditions arising due to the same or the different membership functions and find their own application on adaptive fuzzy control.