Stabilization of Nonlinear Systems : Homogeneous Approach

In this book, we recall some definitions and results on stability and stabilization of nonlinear systems. We generalize Artstein's theorem and we derive sufficient conditions for stabilization of single-input homogeneous systems by means of an homogeneous feedback law. Using some results on manifolds, we establish some conditions for stabilization of single-input homogeneous by dilation systems.In addition, we study the stabilization problem of a class of homogeneous multi-input systems. We give a result for driftless homogeneous systems, then we study the stabilization of homogeneous affine in control systems. Moreover, we study the stabilization problem of homogeneous systems depending on parameter in the autonomous case and we finish by the study of stabilization of homogeneous time varying systems.