  We construct compositional continuous approximations for an interconnection
of infinitely many discrete-time switched systems. An approximation (known as
abstraction) is itself a continuous-space system, which can be used as a
replacement of the original (known as concrete) system in a controller design
process. Having synthesized a controller for the abstract system, the
controller is refined to a more detailed controller for the concrete system. To
quantify the mismatch between the output trajectory of the approximation and of
that the original system, we use the notion of so-called simulation functions.
In particular, each subsystem in the concrete network and its corresponding one
in the abstract network is related through a local simulation function. We show
that if the local simulation functions satisfy a certain small-gain type
condition developed for a network of infinitely many subsystems, then the
aggregation of the individual simulation functions provides an overall
simulation function between the overall abstraction and the concrete network.
For a network of linear switched systems, we systematically construct local
abstractions and local simulation functions, where the required conditions are
expressed in terms of linear matrix inequalities and can be efficiently
computed. We illustrate the effectiveness of our approach through an
application to frequency control in a power gird with a switched (i.e.
time-varying) topology.
