Algorithm for the computation of decentralized fixed modes

The relationship between the residue matrix of the open-loop transfer function of the system and decentralized fixed modes (DFM) is explored. It is shown that there are only (p²-p ¹+1) possible partitions for the control stations where p₁ and p₂ are the number of the stations from which the mode is controllable, and the number of the stations at which the mode is unobservable, respectively. These partitions can be determined from the residue matrix. Nearly decentralized fixed modes (NDFM) are defined in terms of near uncontrollability and near observability and the residues of the subsystems associated with these modes. An algorithm for the computation of both DFM and NDFM is developed. Two examples to illustrate the proposed technique are given