Observer-based control of fully-linearizable nonlinear systems

A study is made of the problem of output feedback control of nonlinear systems that are left-invertible, minimum-phase, and fully linearizable (by static state feedback). The proposed control is an observer-based control in which the state feedback component is a robust, possibly nonlinear, stabilizing state-feedback control law. The observer is designed so that the closed loop system is a two-time-scale singularly perturbed system. However, due to the ε-dependent scaling of the state variables, some of the standard singular perturbation results do not hold for the closed-loop system, in general. The authors present new singular perturbation results on the behavior of the closed-loop system in the presence of such scaling. In particular, they argue that the undesirable effects of such scaling would not arise if the state-feedback control were globally bounded