An algebraic characterization of quotient decentralized fixed modes

In the control of linear time-invariant (LTI) decentralized systems, a decentralized fixed mode (DFM) is one which is immovable using an LTI decentralized controller. However, some DFMs can be moved using more complicated decentralized controllers; the ones which cannot are labelled quotient DFMs (QDFMs), since they arise from a related quotient system. The classical algorithm used to compute the QDFMs requires two steps: a partitioning of the sub-systems, using graph theory, followed by the application of standard tools from decentralized control. Here the goal is to provide a more direct approach to computing them.