Nonlinear systems and differential geometry

Nonlinear systems which are governed by a finite number of ordinary differential equations with controls present constitute a large and important class models for practical purposes. In the last few years, there has been considerable progress in our understanding of this class of models. This is an expository paper devoted to surveying and explaining some of the main results currently available. Background material on manifold theory is included in order to make the paper more nearly self-contained.