Time domain models for multiple time scale linear systems

We study the multiple time scales structure of linear systems of the form x = A0(ε)x + B0(ε)u y = C0(ε)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.