Stability analysis of discrete linear systems with quantized input

In this work, the stability of discrete linear systems under quantized state feedback is addressed. The case with input quantization only is examined here. This case corresponds to the input quantizer having a much lower resolution that the measurement quantizers, and serves as a logical step in understanding the more complicated case of quantization in the input and in the state measurements, treated in a related paper. A simple condition for the origin to be the only equilibrium point is given in terms of the feedback gain. A discrete time formulation of the theory of absolute stability is applied to obtain a stability condition and parameterize feedback gains that result in global asymptotic stability. A numerical example illustrates the application of the method.