Techniques of singular perturbation for system applications

This thesis discusses the techniques of singular perturbation from the engineer's point of view. The technique of singular perturbation is useful for system ana lysis, order reduction, and system control. An explicit form of a singularly perturbed system is derived from a two-time-scale system by properly scaling. By the quasi-steady state approximation or the L-K transformation, two lower order subsystems, slow and fast mode subsystems, are obtained. The propertise of the full order systems, such as stability, controllability, and observability, can be deduced from two lower order systems. Two formulas developed by the author for constructing L and K matrices directly from the eigenvalues are presented. Quasi-steady state approximation and the L-K transformation are evaluated and compared in their applications to order re duction. A modified L transformation is developed here to overcome the existing weaknesses. The effectiveness and merits of three methods for order reduction are shown by the numerical examples.