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In this technical note, exact and approximate solutions of the discrete-time suboptimal proportional-integral-H ∞-estimation problem for affine nonlinear systems using finite-dimensional estimators (filters) are presented. Sufficient conditions for the solvability of the problem are given in terms of discrete-time Hamilton-Jacobi-Isaac's equations. For linear systems, it is shown that, these equations reduce to a system of linear-matrix inequalities. Simulation results are also presented to show the benefit of the new approach.