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This paper focuses on the filter design for nonuniformly sampled nonlinear systems which can be approximated by Takagi-Sugeno (T-S) fuzzy systems. The sampling periods of the measurements are time varying, and the nonuniform observations of the outputs are modeled by a homogenous Markov chain. A mode-dependent estimator with a fast sampling frequency is proposed such that the estimation can track the signal to be estimated with the nonuniformly sampled outputs. The nonlinear systems are discretized with the fast sampling period. By using an augmentation technique, the corresponding stochastic estimation error system is obtained. By studying the stochastic stability and the energy-to-peak performance of the estimation error system, we derive the linear-matrix-inequality-based sufficient conditions. The parameters of the mode-dependent estimator can be calculated by using the proposed iterative algorithm. Two examples are used to demonstrate the design procedure and the efficacy of the proposed design method.