ABSTRACT
A fundamental problem in the theory of systems and control is the mathematical modeling of a physical system. The realistic representation of many systems calls for high-order dynamic equations. The presence of some “parasitic” parameters such as small time constants, moments of inertia, resistances, inductances, and capacitances is often the source for the increased order and “stiffness” of these systems. The stiffness, attributed to the simultaneous occurrence of “slow” and “fast” phenomena, gives rise to “time scales”. The systems in which the suppression of a small parameter is responsible for the degeneration of order (dimension) of the system are labeled as “singularly perturbed” systems, which are a special representation of the general class of time-scale systems. The “curse” of dimensionality coupled with stiffness poses formidable computational complexities for the analysis and control of time-scale systems.
