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In this paper, the problems of quadratic stability conditions and H∞ control designs for Takagi-Sugeno (T-S) fuzzy systems have been studied. First, a new quadratic stability condition, which is more simple than that in a previous paper, has been proposed. Second, two new sufficient conditions in the terms of linear matrix inequalities (LMIs) which guarantee the existence of the state feedback H∞ control for the T-S fuzzy systems have been proposed. The conditions are not only simple but also consider the interactions among the fuzzy subsystems. Finally, based on the LMIs, the H∞ controller designing methods for the T-S fuzzy systems have been given.