Controller-observer scheme for a class of nonlinear singularly perturbed systems

This paper is concerned with the design of a controller-observer scheme for the exponential stabilization of a class of singularly perturbed nonlinear systems based on sliding-modes techniques and nonlinear observers. Under the assumption that only the fast state is available for measurement, an observer design is presented in order to estimate the slow variables. Furthermore, a stability analysis of the closed-loop system is also made to provide sufficient conditions for the exponential stability of the full order closed-loop system when the slow state is estimated by means of the observer. The proposed scheme is applied to the model of a permanent magnet stepper motor in order to illustrate the methodology