Quantized Feedback Control of Discrete-Time MIMO Linear Systems With Input and Output Quantization Over Finite Data Rate Channels

This article considers a control problem of discrete-time multiple-input multiple-output linear systems involving input quantization (for the output of the controller) and output quantization (for the output of the plant). Based on spherical polar coordinate quantizer, a quantization method with finite data rate is proposed for handling the nested quantization and achieving the convergence to the origin of the system with input and output quantization. Further, an optimalization problem is developed for each quantizer, of which the optimal solution set contains a virtual augmented vector. The quantizers quantize their respective virtual augmented vectors to obtain the estimates of the outputs of the plant and the controller. We present the analytical expression of the optimal solution set for each quantizer. Finally, a method is presented to achieve the parameters of the quantizers and the controller.