The paper discusses non-fragile output feedback control design Takagi-Sugeno fuzzy systems with uncertain parameters. In control design for physical systems, there are chances that malfunction in actuator and round-off error of the control gain calculation may occur. Hence, controller gain variations as well as uncertainty in the system parameters should be considered in the control design. For an uncertain fuzzy system, a design method of a non-fragile output feedback controller is proposed by introducing a new type of controllers where the integrals of the membership functions are involved. A non-parallel distributed compensator(Non-PDC) is a generalization of a parallel distributed compensator(PDC), which is a traditional controller for fuzzy systems, and is used for the control design. A non-fragile non-PDC output feedback controller for uncertain fuzzy systems is obtained from new fuzzy multiple Lyapunov functions and its control design conditions are given in terms of a set of linear matrix inequalities(LMIs), which are easily numerically solvable. The descriptor system formulation, which leads to relaxation in controller design conditions, is also employed. These approaches reduce the conservatism of the control design conditions. Finally, numerical examples are given to illustrate our nonlinear control design and to show the effectiveness over other existing results.