Robustness of Output Feedback for a Class of Singularly Perturbed Nonlinear Systems

The authors treat the problem of robustness of output feedback controllers with respect to singular perturbations. Given a singularly perturbed control system whose boundary-layer system is exponentially stable and whose reduced order system is exponentially stabilizable via a (possibly dynamical) output feedback, they present a sufficient condition which ensures that the system obtained by applying the same controller to the original singularly perturbed control system is exponentially stable for sufficiently small values of the perturbation parameter. This condition, which is less restrictive than all those previously given in the literature, is always satisfied when the singular perturbation is due to the presence of fast actuators and/or sensors. Furthermore, it is claimed that, in the linear time-invariant case, if this condition is not satisfied then there exists an output feedback controller which stabilizes the reduced-order system but destabilizes the full-order system.