  In this paper we propose a compositional scheme for the construction of
abstractions for networks of control systems using the interconnection matrix
and joint dissipativity-type properties of subsystems and their abstractions.
In the proposed framework, the abstraction, itself a control system (possibly
with a lower dimension), can be used as a substitution of the original system
in the controller design process. Moreover, we provide a procedure for
constructing abstractions of a class of nonlinear control systems by using the
bounds on the slope of system nonlinearities. We illustrate the proposed
results on a network of linear control systems by constructing its abstraction
in a compositional way without requiring any condition on the number or gains
of the subsystems. We use the abstraction as a substitute to synthesize a
controller enforcing a certain linear temporal logic specification. This
example particularly elucidates the effectiveness of dissipativity-type
compositional reasoning for large-scale systems.
