Quantized control for stochastic system

This paper considers the coarsest quantization control problem. Different from the previous works [4] where the systems are restricted to be deterministic, we focus on the feedback quantization control for general stochastic systems with multiplicative noises. It is showed that the coarsest quantizer that stabilize the multiplicative-noise stochastic system in mean square sense is logarithmic, and the quantization density of which is larger than the results obtained in [4] for deterministic systems for the deterioration of multiplicative noises. Also, we explore that the solvability of the quantizer density is related to a special stochastic linear control problem.