These thesis, done in industrial context with PSA Peugeot-Citroën and IRCCyN, deals with the numerical aspect of the implementation of filters or controllers in embedded processors.The implementation of a controller or a filter in a Finite Word Length context may lead to a deterioration of the global performance, due to parametric errors and numerical noises. We focus here on the effect of the quantization of the embedded coefficients.It exists an infinity of equivalent relalizations of a given controller, and these realizations are no more equivalent in finite precision : classical state-space realizations, delta-realizations, direct forms, observer-state feedback, cascade or parallel decomposition, etc.After having exhibits theses possibilites, this Phd thesis proposes an unifying framework — the implicit specialized state-space — that encompasses usual realizations (and many others unexplored). This specialized form, but still macroscopic, is directly connected to the in-line calculations to be performed and the involved coefficients. Various analysis tools, applied to our formalism, may be used to determine how the realization will be altered during the FWL process (with floating point and fixed point considerations).Then, according to these tools, optimal realizations with the best FWL robustness can be found, via an optimization problem.
