Characterizations of decentralized fixed modes for interconnected systems

A study of the characterization of decentralized fixed modes for large-scale interconnected systems is made. This is done by obtaining a recursive characterization of decentralized fixed modes, in which the existence of fixed modes of a @n-control agent system is expressed in terms of the existence of fixed modes of @n - 1 control agent systems. An interpretation of these conditions is then made in the frequency domain. Simple conditions, in terms of the controllability of the system's subsystems, are then found for a composite system consisting of @n interconnected subsystems to have no decentralized fixed modes. This result clarifies some recent discussion on the fixed modes of interconnected systems; in particular, it proves that Fessas's conjecture is true for systems with two control agents, but false for systems with more than two control agents.

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