Networked control of uncertain systems via the coarsest quantization and lossy communication

We study a networked control problem of uncertain systems based on quantized signals sent over unreliable, lossy communication channels. The coarsest quantization is characterized for attaining the objective of quadratic stability of the overall closed-loop system in a stochastic sense. Our result indicates that the coarsest quantization is given by the logarithmic type and that more information is required through finer quantization for more uncertain systems and more unreliable channels. The characterization provides an analytic upper bound for the coarseness, which is tight for some special cases and generalizes known results for systems without uncertainties and for channels without losses.