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In this paper, we have discussed the full-order robust observer design problem for a class of nonlinear uncertain systems with time-varying delay. The goal of this problem is to design a nonlinear robust observer such that, for time-varying delay and unstructured parameter, the observer can guarantee the observing process robustly stable. A robust nonlinear observer is obtained, the observer gain matrix is included in a Hamiltonian matrix. A numerical example is given to demonstrate the validity of the proposed approach.