Asymptotic Tracking of Discrete-Time Systems Subject to Uniform Output Quantization

This letter explores the internal model principle in order to achieve asymptotic tracking of discrete-time systems subject to output quantization. It is shown that, by artificially quantizing the reference signal, asymptotic tracking can be achieved for a class of systems and references: discrete-time positive real systems, and persistent references in the form of sums of sinusoids. Given the importance of discrete time positive real functions, a systematic way of constructing them is also provided as a contribution. The resulting controller relies on frequency domain tools and may be designed by traditional linear techniques.