Placement of fixed modes by decentralised output feedback control

In this paper we derive a sufficient condition and provide constructive proof for decentralised fixed modes (DFMs) to be quotient fixed mode (QFMs) of LTI systems, and thus are not stabilisable. The conditions are stated in terms of algebraic properties of the system transfer function matrix and whether the DFMs are transmission zeros (TZs) of the quotient subsystems or not. A numerical example is given to illustrate the main results of the paper.