Asymptotic Stability of Quantized Feedback Systems With Input and State Quantizations and Saturations Over Finite Data Rate Channels

This paper considers quantized feedback control of discrete-time linear systems involving quantizations and saturations of the system input and state. A new representation of saturation map is presented by equality with bounded uncertain diagonal matrix and reduces conservatism. Further, based on spherical polar coordinate quantizer, the quantization error is converted to sector-bound uncertainty. Thus, the considered system is modeled as uncertain system and the considered problems are converted into the equivalent solvable problems for uncertain system and the larger stability region is obtained. We firstly propose the quantization methods with finite data rate for asymptotic stability under the system input saturation for two cases: (1) state quantization case, (2) input quantization case. In input quantization case, an augmented vector is constructed and quantized to obtain the estimate of the system input. We further propose the quantization method for the case of quantizations and saturations of the system input and state, which results in nested saturation and nested quantization. In this case, although the quantizer for the sensor output and the quantizer for the controller output can not communicate with each other, by the proposed quantization method, they coordinate with each other to guarantee the asymptotic stability of the systems.