Optimal ρ-realisation for digital controller implementation with stability consideration

The stability robustness problem of a discrete-time feedback system, where the digital controller is implemented with finite word length, is investigated. Based on a polynomial operator approach a new sparse controller realisation, called ρ-realisation, is derived. The problem of finding optimal ρ-realisations is solved. A numerical example is given, which shows that the optimised structure outperforms the fully parametrised optimal realisation.