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A novel fuzzy neural network (FNN) quadratic stabilization output feedback control scheme is proposed for the trajectory tracking problems of biped robots with an FNN nonlinear observer. First, a robust quadratic stabilization FNN nonlinear observer is presented to estimate the joint velocities of a biped robot, in which an H∞ approach and variable structure control (VSC) are embedded to attenuate the effect of external disturbances and parametric uncertainties. After the construction of the FNN nonlinear observer, a quadratic stabilization FNN controller is developed with a robust hybrid control scheme. As the employment of a quadratic stability approach, not only does it afford the possibility of trading off the design between FNN, H∞ optimal control, and VSC, but conservative estimation of the FNN reconstruction error bound is also avoided by considering the system matrix uncertainty separately. It is shown that all signals in the closed-loop control system are bounded.