Robust control algorithms and software implementation.

Summary We present the different algorithms of robust control and more particularly those leading to the synthesis of the h-infinite control. The robust control problems are put in the form of a so-called standard problem which consists in augmenting the nominal system taking into consideration the required robustness specifications, then minimizing a criterion of a frequency nature of quadratic or infinite type. There are two different approaches to designing the h-infinite controller. Nehari's approach consists in finding the projection of an anti-stable system on the space of stable systems with the h-infinite norm. Glover's approach, also called ultra-modern, consists in solving two Riccati equations and then putting the controller in a descriptor form. The algorithm that is presented and implemented in the thesis is an improvement of Glover's method leading to more robust calculations. The robust control algorithms have been implemented in Basile, a software for automatic control. A library of Basile macros has been realized allowing to solve standard h-infinite problems and more generally, to study the robustness of linear systems. In order to validate the algorithms and to give examples of h-infinite problems, academic and industrial applications (aircraft, satellite) are treated in detail.