Abstract : A specialised implicit state-space representation is introduced to deal
with finite wordlength effects in controller implementations. This
specialised implicit form provides a macroscopic description of the
algorithm to be implemented. So, it constitutes a unifying framework,
allowing to encompass various implementation forms, such as the
delta-operator, the rho Direct Form II transposed, observer-based and many
other realisations usually considered separately in the literature.
Different measures quantifying the finite wordlength effects on the
overall closed-loop behaviour are defined in this new context. They
concern both stability and performance. The gap with the infinite
precision case is evaluated classically through the coefficient
sensitivity and roundoff noise analysis. The problem of determining a
realisation with minimum finite wordlength effects can subsequently be
solved using appropriate numerical methods. The approach is illustrated
with an example.