Decentralized Retunability under Structural Perturbations

A model of interconnected systems, with each subsystem having access to its local states is considered. It is assumed that structural perturbations may occur, where each subsystem or group of subsystems may be connected or disconnected. Two related problems, that of decentralized fixed modes and the solution to the decentralized servo-mechanism problem is analyzed. Conditions are given under which the interconnected system remains decentrally stabilizable and retunable under the structural perturbations. It is shown that these conditions are intimately related to the graph of the system and specifically to all "strongly connected subgraphs."