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This paper presents an integrated algorithm of fuzzy modeling and controller design. An LMI condition to identify the parameters of a Takagi-Sugeno fuzzy model (T-S fuzzy model) is derived. More importantly, we achieve stable fuzzy control for the identified T-S fuzzy model. The fuzzy modeling and controller design are applied to vision tracking control using a two-link manipulator with a CCD camera. The experimental results show the utility of the proposed integrated algorithm of fuzzy modeling and controller design.