Algebraic characterization of decentralized fixed modes and pole assignment

An input-output, frequency domain characterization of decentralized fixed modes is given in this paper, using only standard block-diagram algebra, well-known determinantal expansions and the Binet-Cauchy formula. Using this characterization, an algebraic proof is presented of the fact that, in a strongly connected system, spectrum assignment (stabilization) is possible using decentralized dynamic compensation if and only if the system has no fixed modes (only stable fixed modes).