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In this paper, the problems of quadratic stabilization conditions for Takagi-Sugeno fuzzy systems have been studied. A new quadratic stability condition, which takes into account the knowledge of the membership functionpsilas shape by considering bounds on their cross products, has been proposed. And then a new sufficient condition in terms of linear matrix inequalities is developed to synthesize the state feedback controller that stabilizes the fuzzy systems. An numerical example is provided to illustrate the effectiveness of the proposed results.