Designing Low Parametric Sensitivity FWL Realizations of LTI Controllers/Filters within the Implicit State-Space Framework

The problem of Finite Word Length (FWL) implementation of Linear Time Invariant (LTI) filters or controllers is considered in this paper. A specialized implicit state-space representation enabling a macroscopic description of the algorithm to be implemented is exhibited. It constitutes a unifying framework to encompass various implementation form, such as q, δ, the observer-based and other realizations. This paper formalizes especially the problem consisting to analyze the parametric sensitivity of such realizations, and then to optimize them in order to limit deteriorations along the process of FWL implementation. The sensitivity of some structured realizations with respect to the coefficients involved and the computation effort are compared on an example.