Time domain models for multiple time scale linear systems

We study the multiple time scales structure of linear systems of the form x = A0(??)x + B0(??)u y = C0(??)x with a view to obtaining ´approximate´ lower order dynamical models valid at different time scales. Our development includes the classical two time-scale case. We use our results to study the robustness of the positive realness of linear systems systems under singular perturbations.