Singular perturbations and time-scales

Abstract

This chapter has introduced the so-called explicit singular perturbation form of two-time-scale systems. This form is natural for systems whose two-time-scale behavior is due to the presence of small and large storage elements, such as capacitors, masses, etc. The singular perturbation parameter represents the ratio of the time constant of a representative small storage element versus the time constant of a representative large storage element.

Other less obvious causes of two-time-scale behavior may lead to some "hidden" rather than the explicit singular perturbation forms. The next chapter deals with some of these forms.