Characterization of structured and unstructured decentralized fixed modes using transfer matrices

In this paper, structured and unstructured decentralized fixed modes (DFMs) are studied for a decoupled controllable and observable strictly proper linear time-invariant system with distinct poles. The conditions characterizing both structured and unstructured DFMs for the case of three single-input single-output (SISO) control stations are analytically developed, and the results are then interpreted in terms of the system transfer function matrix. It is shown how mutual couplings between local control stations can influence the structured and unstructured DFMs of the overall decentralized system. Supplementary remarks throughout the paper describe the general case with any arbitrary number of SISO control stations.