Nonholonomic systems and exponential convergence: some analysis tools

In this paper the authors make a contribution to the analysis of nonholonomic systems with exponential rates of convergence. A key idea is the use of control laws which render the closed loop system homogeneous with respect to a dilation. The analysis is applied to nonholonomic systems in power form and consists of two steps. The first step is a reduction to an invariant set and then the application of an averaging result. The averaging theorem is a stability result for C^0 homogeneous order zero vector fields