Exact linearization and zero dynamics

The authors address the problem of designing feedback laws which render a given nonlinear system locally diffeomorphic to a linear and controllable one. The philosophy underlying work on this topic is essentially that if there exists a (natural) choice of output functions such that the system is invertible and the zero dynamics are trivial, then at each point of an open and dense subset of the state space, it is possible to define a dynamic state feedback which renders a given nonlinear system locally diffeomorphic to a linear and controllable one. The authors review this philosophy in more detail, provide a number of interesting additional results, and comment about the problem of establishing verifiable conditions under which output functions satisfying the stated requirements do exist. The concept of zero dynamics and some facts related to system invertibility are reviewed. A number of applications in which this design philosophy was successfully implemented are summarized