  We address the link between the controllability or observability of a
stochastic complex system and concepts of information theory. We show that the
most influential degrees of freedom can be detected without acting on the
system, by measuring the time-delayed multi-information. Numerical and
analytical results support this claim, which is developed in the case of a
simple stochastic model on a graph, the so-called voter model. The importance
of the noise when controlling the system is demonstrated, leading to the
concept of control length. The link with classical control theory is given, as
well as the interpretation of controllability in terms of the capacity of a
communication canal.
