Asymptotic stability of nonlinear singularly perturbed systems using higher order corrections

Abstract

This paper examines a methodology for investigating the asymptotic stability properties of nonlinear singularly perturbed systems. This is achieved by constructing the so-called zeroth order model (uncorrected model). Based on this model a weighted scalar sum of the Lyapunov functions for two lower order subsystems is obtained. The estimates of the region of attraction and the upper bound on the perturbed parameter are established. It is shown that by extending this methodology to higher order corrected models, less conservative results are obtained. These considerable improvements are facilitated by introducing a new fast variable in both uncorrected and corrected models.