Analysis of sensitivity measures of finite-precision digital controller structures with closed-loop stability bounds

The problem of digital controller structures and the effect of finite-word-length (FWL) implementation on the closed-loop stability of digital feedback control systems is addressed. A framework is presented to derive two lower stability bounds for a closed-loop system, which are controller structure dependent, and then to solve the optimal FWL controller structure problem by maximising one of these lower bounds. This yields an improved method to design optimal finite-precision controller structures with better numerical accuracy and closed-loop stability characteristics. Comparisons using numerical examples from two digital controller structures demonstrate that the procedure proposed for the more efficient measure yields an improved finite controller realisation with combined lower bits and higher lower stability bounds