Singularly Perturbed Weakly Coupled Linear Control Systems

Abstract

In mathematical models of many real physical systems small parameters appear. Two large classes of small parameter problems have been studied so far, extensively in the context of control theory: 1) singularly perturbed systems (Kokotovic et al. , 1986; Gajic et al. , 1990) and 2) weakly coupled systems (Gajic et al. , 1990). However, motivated by the models of the real physical systems, we have found that many of them have both singularly perturbed and weakly coupled structures. Even more, the structure of many systems with slow-fast phenomena and weak coupling can not be put either in the standard singularly perturbed or standard weakly coupled forms. In this chapter, we study systems that are at the same time both singularly perturbed and weakly coupled.