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A piecewise-linear (PWL) circuit model of hysteresis phenomena is presented. The proposed model involves the use of parallel-connected simple PWL circuits. The PWL characteristic of the model allows a direct determination of the condition on a rate-independent hysteresis behavior. The basic features of the model are discussed through proper demonstrations. In particular, it is shown that the parameters of the PWL circuit model can be set by using an identification theorem that ensures an arbitrary precision (ε-approximation). The theorem results from the generalization of analogous theorems for single-valued functions to many-valued functions. Finally, both numerical comparisons with other models and experimental fittings are presented to verify the robustness of the ε-approximation theorem to finite-precision arithmetic.