In this paper, we study nonparametric density estimation from quantized samples. Since quantization decreases the amount of information, interpolation (or estimation) of the missing information is needed. To achieve this, we introduce sampled-data H∞ control theory to optimize the worst case error between the original probability density function and the estimation. The optimization is formulated by linear matrix inequalities and equalities. A numerical example is illustrated to show the effectiveness of our method.