  The purpose of this report is to define abstractions for multi-agent systems
under coupled constraints. In the proposed decentralized framework, we specify
a finite or countable transition system for each agent which only takes into
account the discrete positions of its neighbors. The dynamics of the considered
systems consist of two components. An appropriate feedback law which guarantees
that certain performance requirements (eg. connectivity) are preserved and
induces the coupled constraints and additional free inputs which we exploit in
order to accomplish high level tasks. In this work we provide sufficient
conditions on the space and time discretization of the system which ensure that
we can extract a well posed and hence meaningful finite transition system.
