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This work deals with the equilibrium point and stability analysis of discrete linear systems under quantized feedback. The case of quantized state feedback based on quantized state measurements (QIQM) is treated here. Unlike the case of input quantization (QI) only, there is no closed-form solution for the equilibrium points. However, a computable condition for the origin to be the only equilibrium is given. The stability analysis requires the construction of an equivalent system and a stability theorem for systems with a sector nonlinearity that is multiplicatively perturbed by a bounded function of the state. The analysis reduces to a simple test in the frequency domain, namely, the closed-loop system is globally asymptotically stable about the origin if the Nyquist plot of a system transfer function lies to the right of a vertical line whose abscissa depends on the 1-norm of the feedback gain. A numerical example of the analysis technique and some guidelines for the synthesis of a stable feedback gain are also provided.