Interesting Phenomena in the Synchronisation of Disturbed Systems

This paper presents three interesting phenomena that occur in the synchronisation of disturbed systems. The first phenomenon describes the necessity that dynamical local controllers have to be used to introduce the model of the disturbances into each of the extended agents. This result extends the Internal-Model Principle from multivariable control to multi-agent systems. A necessary and sufficient synchronisation condition is given. The second phenomenon concerns the fact that the internal disturbance models of all agents modify the synchronous trajectory of the overall system. For specific initial states the synchronous trajectory is completely fixed by the disturbance models and does not reflect the properties of the agents. This fact leads to the third phenomenon that indicates that an undisturbed virtual agent has to be introduced into the overall system to ensure that the synchronous trajectory is generated by the agent dynamics like in undisturbed multi-agent systems. The considered phenomena are illustrated by numerical examples.