The mathematical model relies on a switching function
that depends on a priori
values 
and a posteriori
values 
.
The semantics are specified by
the recursive relation between
and 
which takes the form
Note the 
subscript in 
.
If is independent of 
,
this results in the general sequence
In this sequence, each mode, , may be departed when any of the
three assignment statements is executed.
In the model in
Fig. 2b this corresponds to additional feedback of 
into 
which introduces a loop between g and .
Overall, three cases can be distinguished (Fig. 6):
leads to
.
Because of the immediate transition when is calculated,
the assignment 
is not executed, and, therefore, this
mode does not affect x.
results in
.
As soon as x is updated as represented by the 
element,
the mode is departed, and, therefore, it only
exists at a point in time.
results in
.
After a period of continuous evolution, the mode is departed.
Figure 6: Classes of modes of operation.
