Structural Completeness of a Multichannel Linear System With Dependent Parameters

It is well known that the “fixed spectrum” (i.e., the set of fixed modes) of a multichannel linear system plays a central role in the stabilization of such a system with decentralized control. A parameterized multichannel linear system is said to be “structurally complete” if it has no fixed spectrum for almost all parameter values. Necessary and sufficient algebraic conditions are presented for a multichannel linear system with dependent parameters to be structurally complete. An equivalent graphical condition is also given for a certain type of parameterization.