ABSTRACT
Singularly perturbed (ODE) systems arise as models of a wide variety of chemical processes, biochemical systems, electrical circuits and power systems, etcetera, whose dynamic behavior exhibits time-scale multiplicity. There is, as one may expect, an inherent connection between differential algebraic equations and singularly perturbed systems. There is a vast literature on the application of singular perturbation theory for the analysis and control of systems with multiple time scales, in particular two time scales, For nonlinear two-time-scale systems, it is well-established that standard inversion-based controllers, designed without explicitly addressing the time-scale multiplicity, are often ill-conditioned and may lead to instability. Singular perturbation theory allows addressing the control of two-time-scale systems through a systematic decomposition of the system dynamics in different time scales. The derivation of the standard singularly perturbed representation of the rate-based ODE models allows the application of available results on stability analysis and control for two-time-scale systems.
