Input-output description of linear systems with multiple time-scales

It is pointed out that the study of systems evolving at multiple time-scales is simplified by studying reduced-order models of these systems valid at specific time-scales. The present investigation is concerned with an extension of results on the time-scale decomposition of autonomous systems to that of input-output systems. The results are employed to study conditions under which positive realness of a transfer function is preserved under singular perturbation. Attention is given to the perturbation theory for linear operators, the multiple time-scale structure of autonomous linear systems, the input-output description of two time-scale linear systems, the positive realness of two time-scale systems, and multiple time-scale linear systems.