On Computing Quotient Decentralized Fixed Modes

In the decentralized control of linear time-invariant (LTI) systems, the notion of decentralized fixed modes (DFMs) was introduced to capture those modes which are immovable using LTI controllers. However, some DFMs can be moved using more complicated controllers. Recently a so-called “quotient system” associated with the original plant was investigated and it was proven that its DFMs, which we label quotient DFMs (QDFMs), are exactly those DFMs of the original system which cannot be moved using any form of nonlinear time-varying (NLTV) controller. The algorithm provided there to compute the QDFMs requires two steps: first, a partitioning of the sub-systems, using graph theory, and then application of standard tools from decentralized control. However, the first step is fragile, so the goal here is to provide a more robust approach to computing the QDFMs.