  This paper formulates a framework for the analysis and distributed control of
interconnected systems from the behavioural perspective. The discussions are
carried out from the viewpoint of set theory and the results are completely
representation-free. The core of a dynamical system can be represented as the
set of all trajectories admissible through the system and interconnections are
interpreted as constraints on the choice of trajectories. We develop a
structure in which the interconnected behaviour can be directly built from the
behaviours of the subsystems in an explicit way without any presumed forms of
representations. We show that the interconnected behaviour can also be fully
obtained from local observations of the subsystem. Furthermore, we develop the
necessary and sufficient conditions for the existence of distributed controller
behaviours and their explicit construction. Due to the entirely
representation-free nature of this framework, it unites various representations
and descriptions of features of dynamical systems (e.g. models, dissipativity,
data, etc.) as behaviours, allowing for the formation of a unified platform for
the analysis and distributed control for interconnected systems.
