Various notions of linearization of nonlinear control systems: concepts, methods, applications

For each notion of linearization, we will give necessary and sufficient conditions for linearizability (if they exist) and provide methods to find linearizing transformations. Describing linearizable system will require some tools from differential geometry, like Lie brackets, vector distributions and their involutivity. We will introduce them and show that they appear in nonlinear control theory in a natural way. We will illustrate the presented results with the help of physical, mainly mechanical, examples.