Stabilization of time-varying singularly perturbed systems by observer-based slow-state feedback

This note develops an observer based on the slow reduced-order system of a time-varying full-order system. An upper bound μ^*on the singular perturbation parameter μ is derived such that for μ smaller than μ^*, the full-order system is stabilized by linear feedback of the observed slow state. The dependence of this bound on the system matrices and the observer and controller gain matrices is discussed.