  We develop a switched predictor-feedback law, which achieves global
asymptotic stabilization of linear systems with input delay and with the plant
and actuator states available only in (almost) quantized form. The control
design relies on a quantized version of the nominal predictor-feedback law for
linear systems, in which quantized measurements of the plant and actuator
states enter the predictor state formula. A switching strategy is constructed
to dynamically adjust the tunable parameter of the quantizer (in a piecewise
constant manner), in order to initially increase the range and subsequently
decrease the error of the quantizers. The key element in the proof of global
asymptotic stability in the supremum norm of the actuator state is derivation
of solutions' estimates combining a backstepping transformation with small-gain
and input-to-state stability arguments, for addressing the error due to
quantization. We extend this result to the input quantization case and
illustrate our theory with a numerical example.
