Minimum Capacity in Stabilizing an LTI System with Quantized Control Inputs via Output Feedback

This paper studies the design constraints from network channel in stabilizing a linear time-invariant (LTI) discrete-time system. In the system, the control inputs are quantized and then transmitted through a noise free channel to the remote plant. The quantization error is modeled as a product of the source signal of quantizer and a white noise. The latter is refereed to as the relative quantization error in this work. The channel capacity is measured in terms of the variance of the relative quantization error (or the signal-to-noise ratio of the input channel). The lower bound of the total capacity of all control input channels for stabilizing an LTI minimum phase plant with quantized control inputs via output feedback is found. This lower bound is determined by the product of unstable poles of the plant. This minimum total capacity shows the trade-off among the capacities of control input channels (or the variances of the relative quantization errors) of the system.