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A Lyapunov-based approach is used to derive a sufficiency condition for stabilizing a class of fuzzy system models using linear controllers. A design algorithm for constructing stabilizing linear controllers is given. The results obtained are illustrated with a design of a linear stabilizing controller for a system consisting of an inverted pendulum mounted on a cart. The controller is designed using a fuzzy model of the system and tested on the original system model.
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Stanisław H. Żak (1999) studied this question.
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