Singular perturbation modelling of continuous and discrete physical systems

The major shortcoming of the singular perturbation theory preventing its application to practical problems is that the system described by state equations is seldom given in the singularly perturbed form. This paper presents a systematic procedure which converts the state equations of a large scale time invariant system to singularly perturbed form, assuming that, such a classification is possible. This is accomplished by appropriate scaling and grouping of the state variables into slow and fast groups, while retaining as many physical state variables as possible in the new state description. An improved slow-fast grouping of the states can result by allowing linear combination of certain available physical variables as new state variables. Several examples are given to illustrate the method.