A closed-loop principal component analysis of singularly perturbed systems

Singularly perturbed, or more generally "weakly coupled," systems are examined in the light of the "closed-loop principal component analysis." This is a technique which determines the "principal" state coordinates of a system closed up by an LQG loop, and classifies these coordinates by order of importance. By a numerical exploration, it is shown that the "closed-loop principal component analysis" is consistent with the splitting of the singularly perturbed system into a slow (main) and a fast (parasitic) mode.