This paper deals with the stability analysis problem of discrete‐time polynomial systems subject to input quantization. The quantizer under consideration is supposed to be dynamic. Indeed, considering the quantization error as bounded disturbances, the regional input‐to‐state stability is studied. The approach developed consists in characterizing two nested invariant sets where the outer one is a region of attraction and the inner one is the robust invariant set with respect to the quantization error. By defining a performance index between the quantized system and the quantizer‐free system, a quasi‐convex problem is formulated to minimize an upper bound on such a performance index.