How much information is needed in quantized nonlinear control?

Quantization rate is a crucial measure of complexity in determining stabilizability of control systems subject to quantized state measurements. This paper investigates quantization complexity for a class of nonlinear systems which are subjected to disturbances of unknown statistics and unknown bounds. This class of systems includes linear stablizable systems as special cases. Two lower bounds on the quantization rates are derived which guarantee input-to-state stabilizability for continuous-time and sampled-data feedback strategies, respectively. Simulation examples are provided to validate the results.