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In this paper, the problems of relaxed quadratic stability conditions and H∞ output feedback control designs for T-S fuzzy systems have been studied. First new quadratic stability conditions are obtained by relaxing the stability conditions derived in previous papers. Secondly it presents H∞ output feedback control designs of complex nonlinear systems which can be represented by T-S fuzzy dynamic systems. Based on a common Lyapunov function, new output feedback H∞ fuzzy control design methods are developed. New method considers the interactions among all fuzzy subsystems. The output feedback H∞ controllers can be obtained by solving a set of suitable linear matrix inequalities.