An analysis for sampled-data systems with quantization and quantizer design

Abstract

In digital control, we have to quantize the signal. Since quantizing is a nonlinear operation, its analysis is difficult. Often we linearize the quantizer by an additive noise model. We study a stability and performance analysis of sampled-data systems with quatization which is designed by using the linearization. We show that if the linear model is stable, the states of the real system are bounded, and if the linear model has small L² gain, the real system has small power gain. We apply the results to the design for a quantizer which is called differential pulse code modulation (DPCM)..