Decentralized Stabilization of Large Scale Systems by Frequency Domain Methods

A notion of weak coupling between subsystem of a large-scale system is developed based on a sufficient condition for a linear, time-invariant MIMO systems. The weak coupling measure provides a frequency dependent requirement on the system response for stability of a decentralized controller for the system. An abstract notion of a generalized Nyquist criterion for MIMO systems (as discussed in Brockett and byrnes [7] ) is extended for decentralized feedback control. Computational methods are provided which exploit a connection between a gap-metric and the principal angles between pairs of subspaces. The principal angles are shown to be related to the singular values of an easily conputed matrix.