The purpose of this work is the study of stability and robustness properties of nonlinear systems using homogeneity-based methods. Firstly, we recall the usual context of homogeneous systems as well as their main features. The sequel of this work extends the homogenization of nonlinear systems, which was already defined in the framework of weighted homogeneity, to the more general setting of the geometric homogeneity. The main approximation results are extended. Then we develop a theoretical framework for defining homogeneity of discontinuous systems and/or systems given by a differential inclusion. We show that the well-known properties of homogeneous systems persist in this context. This work is continued by a study of the robustness properties of homogeneous or homogenizable systems. We show that under mild assumptions, these systems are input-to-state stable. Finally, the last part of this work consists in the study of the example of the double integrator system. We synthesize a finite-time stabilizing output feedback, which is shown to be robust with respect to perturbations or discretization by using techniques developed before. Simulations conclude the theoretical study of this system and illustrate its behavior
