  We study feedback control for discrete-time linear time-invariant systems in
the presence of quantization both in the control action and in the measurement
of the controlled variable. While in some application the quantization effects
can be neglected, when high-precision control is needed, they have to be
explicitly accounted for in control design. In this paper we propose a switched
control solution for minimizing the effect of quantization of both the control
and controlled variables in the case of a simple integrator with unitary delay,
a model that is quite common in the computing systems domain, for example in
thread scheduling, clock synchronization, and resource allocation. We show that
the switched solution outperforms the one without switching, designed by
neglecting quantization, and analyze necessary and sufficient conditions for
the controlled system to exhibit periodic solutions in the presence of an
additive constant disturbance affecting the control input. Simulation results
provide evidence of the effectiveness of the approach.
