Right-invertibility for a class of nonlinear control systems: A geometric approach

In recent years it has become evident that various synthesis problems known from linear system theory can also be solved for nonlinear control systems by using differential geometric methods. The purpose of this paper is to use this mathematical framework for giving a preliminary account on the notion of right-invertibility of a nonlinear system. This concept, which is of importance in several tracking problems, requires a Taylor-series expansion of the output function. We will also show that there is an appealing geometric interpretation of the lower-order terms in this series expansion. In this way a function that can occur as output function of a nonlinear system is partly described by specifying its k-jet.