A system is said to be robust if it is possible to guarantee his dynamic behaviour despite dispersion of his features due to production, environmental changes or aging. beyond the fact that a dispersion is ineluctable, a greater one allows to reduce production costs. Thus, considering robustness is a crucial stake during the conception of a system.Robustness can be achieved using feedback, but is more difficult in Open-Loop, which concerns estimator synthesis for instance.Robustness is a major concern of the Robust Control Community. Many tools have been developed to analyse robustness of a system towards a set of uncertainties (μ analysis for instance). And even if the problem is known to be difficult (speaking of complexity), sufficient conditions allow to formulate results to test the robust stability of a system. Thanks to the development of interior point methods, the emergence of optimization under Linear Matrix Inequalities Constraints allows to test these results using an efficient algorithm.Based on these analysis results, the robust controller synthesis problem cannot be recast as a convex optimization problem involving LMI. But for some cases such as filter synthesis, the synthesis problem can recast as a convex optimization problem. This fact let sense that robust control tools have some potential for estimators synthesis.Exploiting this fact, this thesis ofiers a complete approach of robust estimator synthesis, using robust control tools, while keeping what made the nominal approaches successful : eficient computation tools. this approach goes through reinterpretation of nominal estimation using LMI optimization, then propose a systematic extension of these tools to robust estimation.This thesis presents not only synthesis tools, but also analysis tools, allowing to test the robust performance reached by estimators All the results are proposed as convex optimization problems involving LMI.As a conclusion, robust estimator synthesis problems belong to a wider class of problems : robust open-loop synthesis problems, which have a great potential in many applications. Basic results are formulated for open-loop synthesis, providing results for cases where feedback cannot be used. An extension to LPV systems with an application to sensorless control is given.
