  This paper formulates and studies the concepts of approximate (alternating)
bisimulation relations characterizing equivalence relations between
interconnected systems and their abstractions. These equivalence relations
guarantee that the symbolic model conserves the original model's dynamics. We
develop a compositional approach for abstraction-based controller synthesis by
relying on the notions of approximate composition and incremental
input-to-state stability. In particular, given a large-scale system consisting
of interconnected components, we provide conditions under which the concept of
approximate (alternating) simulation relation is preserved when going from the
subsystems to the large-scale interconnected system. The engineering relevance
of the theoretical results has been evaluated through an application in traffic
congestion control.
