Stabilization of a discrete time linear system over finite data-rate channel with noise attenuation performance by spherical polar coordinate quantizer

This paper considers the problem of achieving the first moment stability and the given noise attenuation performance of a discrete time linear system with unbounded noise. Based on spherical polar coordinates, a quantizer is proposed with a definite relation between the quantized data and the corresponding quantization error. And a necessary and sufficient condition for the first moment stability of the system is presented. Further, based on the quantizer, two coding schemes are proposed for time-varying data rate and fixed data rate respectively, which achieve both the first moment stability and the noise attenuation performance of the system with unbounded noise.