Robust Feedback Linearization of Uncertain Nonlinear Systems

We present a result on the robust stabilization of a class of nonlinear systems exhibiting parametric uncertainty. Consider a nonlinear system with a vector of unknown parameters perturbed about a known value. A Taylor series of the system about the nominal parameter vector coupled with a feedback linearizing control law yields a linear system plus nonlinear perturbations about the nominal parameters. Via a structure matching condition, a Lyapunov based control law is shown to stabilize the full system. The novelty of the result is that the linearizing coordinates are completely known since they are defined about the nominal parameter vector.