As shown,
time scale abstraction collapses behavior during small intervals
into pinnacles which
is modeled by switching based on a priori
state values.
In contrast, parameter abstraction
is modeled by switching conditions based on
a posteriori state values.
The mythical modes that result from these conditions are modeling
artifacts and have no real representation, and, therefore, do not
affect the state vector, x. This is called the principle of
invariance of state [3] which allows
mythical modes to be
replaced by immediate transitions to the final real mode (either
a pinnacle, 
, or a continuous mode, 
).
However, this can be a complex task [4] and
introduces global knowledge into local switching conditions which
obscures effects of local switching conditions.