On weak relative degree and the McGehee transformation

The authors analyze closed-loop systems that represent the internal dynamics of a nonlinear system, after the linearizing control u* has been applied. In keeping with the nomenclature of input-output linearization, they define internal dynamics to include the transient behavior of the system enroute to the zero dynamics submanifold. When the relative degree is weak, a certain class of internal dynamics has a singularity which is the preimage of an equilibrium point located at infinity. The McGehee transformation moves this point to a saddle equilibrium point at the origin