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It has been widely accepted that a hysteretic system can be controlled by combining inverse compensation with feedback. Among the strategies to identify hysteretic systems, data-driven models have been received great attention due to its flexibility and ability to online and adaptive estimation. Nevertheless, less attention has been paid to determine its inversion, which is essential to use such models in control applications. The novelty of this paper is twofold. First, we propose a method to obtain analytically the inverse compensation of a hysteretic system modeled by a Nonlinear Auto-Regressive Model with eXougenous input (NARX) representation with a bounding structure. Second, this paper presents an adapted nonautonomous electronic circuit with rate-independent hysteresis and linear dynamics, which is used as a benchmark to test the proposed methodology. The experimental results have shown the efficiency of the proposed technique.