A multiple Lyapunov function approach to stabilization of fuzzy control systems

Authors:
K. Tanaka;T. Hori;H. O. Wang
Affiliations:
Dept. of Mech. Eng. & Intelligent Syst., Univ. of Electro-Commun., Tokyo, Japan;-;-
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2003

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Abstract

This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. Based on the fuzzy Lyapunov function approach, we give stability conditions for open-loop fuzzy systems and stabilization conditions for closed-loop fuzzy systems. To take full advantage of a fuzzy Lyapunov function, we propose a new parallel distributed compensation (PDC) scheme that feedbacks the time derivatives of premise membership functions. The new PDC contains the ordinary PDC as a special case. A design example illustrates the utility of the fuzzy Lyapunov function approach and the new PDC stabilization method.