Journal
IEEE TRANSACTIONS ON FUZZY SYSTEMS
Volume 11, Issue 4, Pages 582-589Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2003.814861
Keywords
fuzzy control; fuzzy Lyapunov function; nonlinear systems; stabilization
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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.
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