On the Effect of Quantization on Performance

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Vijay Gupta, Amir F. Dana, Richard M Murray, Babak Hassibi
Submitted, 2006 American Control Conference

We study the effect of quantization on the performance of a scalar dynamical system. We provide an expression for calculation of the LQR cost of a dynamical system for a general quantizer. Using the high-rate approximation, we evaluate it for two commonly used quantizers: uniform and logarithmic. We also provide a lower bound on performance of the optimal quantizer based on entropy arguments and consider the case when the channel drops data packets stochastically.