  This paper extends the $l$-complete approximation method developed for time
invariant systems to a larger system class, ensuring that the resulting
approximation can be realized by a finite state machine. To derive the new
abstraction method, called asynchronous $l$-complete approximation, an
asynchronous version of the well-known concepts of state property, memory span
and $l$-completeness is introduced, extending the behavioral systems theory in
a consistent way.
