When using techniques to design de-centralized controllers for large systems, the whole system is divided into subsystems which are analysed using control theory before being re-combined. An analogy is established with substructural analysis in structural mechanics, in which ∞H∞H∞H de-centralized control theory corresponds to substructural modal synthesis theory so that the optimal parameter 2crγ− of the whole system corresponds to the fundamental vibration frequency of the whole structure, here crγ is the optimal ∞H induced norm of the whole system, and its determination is a key step in the design of ∞H de-centralized control systems. Hence modal synthesis methodology and the extended Wittrick-Williams