A comparison of multiple time-scale analysis and overlapping decompositions

Two-level hierarchical systems are considered, and two different design methodologies, multiple-time-scale analysis and overlapping decompositions, are compared. The comparison is based on quadratic performance indices. It is demonstrated that, in general, the multiple-time-scale approach, produces better results whenever the time-scale parameter is small. However, the overlapping decompositions approach usually yields better controller designs as the time-scale parameter gets larger. An example of a mass-spring system is presented to illustrate the practical applications of the theoretical details discussed.