Exponentially convergent control laws for nonholonomic systems in power form

This paper introduces a method for constructing exponentially convergent control laws for n-dimensional nonholonomic systems in power form. The methodology is based on the construction of a series of nested invariant manifolds for the closed-loop system under a linear control law. A recursive algorithm is presented which uses these manifolds to construct a three-dimensional system in power form. It is shown that the feedback controller for the original system is the one for this three-dimensional system with a proper choice of the gains.