Maintaining Robust Stability and Performance through Sampling and Quantization

The inherent problem with continuous-time robust control synthesis is that it returns a controller which cannot directly be implemented on a numeric device. The discrete-time robust control synthesis does not fully solve this problem, as the sampling rate is considered as an input hyperparameter, without explicitly performing a selection, and the quantization of the controller coefficients is not encompassed in the synthesis procedure. The aim of this paper is to provide rigorous means to efficiently compute the sampling rate and quantization step for a given continuous regulator in order to maintain the robust stability and robust performance specifications guaranteed in the analog domain, assuming a constant rate and fixed-point arithmetic, using the structured singular value framework and global optimization techniques. A numerical example is further presented and discussed, emphasizing practical implications.