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

Abstract

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.