Dynamics of strongly coupled symmetric composite systems†

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Abstract
Dynamical systems composed of symmetrically interconnected identical subsystems are modelled and analysed. It is shown that the performance of the subsystems operating within the whole system can be exactly described by a state-space model of order twice the order of the isolated subsystem. Because of the conformity of the subsystem performance this is true even for strong interactions. The controllability, observability and existence of decentralized fixed modes can be tested by means of low-order models. Considering systems with an asymptotically infinite number of subsystems, necessary and sufficient conditions are derived on the subsystem dynamics and the interconnections for being cooperative. The results are utilized to study the performance of symmetric power systems.