<s>
In	O
systems	O
theory	O
,	O
a	O
realization	B-Application
of	O
a	O
state	O
space	O
model	O
is	O
an	O
implementation	O
of	O
a	O
given	O
input-output	O
behavior	O
.	O
</s>
<s>
For	O
a	O
linear	O
time-invariant	O
system	O
specified	O
by	O
a	O
transfer	O
matrix	O
,	O
,	O
a	O
realization	B-Application
is	O
any	O
quadruple	O
of	O
matrices	B-Architecture
such	O
that	O
.	O
</s>
<s>
This	O
state-space	O
realization	B-Application
is	O
called	O
controllable	O
canonical	O
form	O
(	O
also	O
known	O
as	O
phase	O
variable	O
canonical	O
form	O
)	O
because	O
the	O
resulting	O
model	O
is	O
guaranteed	O
to	O
be	O
controllable	O
(	O
i.e.	O
,	O
because	O
the	O
control	O
enters	O
a	O
chain	O
of	O
integrators	O
,	O
it	O
has	O
the	O
ability	O
to	O
move	O
every	O
state	O
)	O
.	O
</s>
<s>
This	O
state-space	O
realization	B-Application
is	O
called	O
observable	O
canonical	O
form	O
because	O
the	O
resulting	O
model	O
is	O
guaranteed	O
to	O
be	O
observable	O
(	O
i.e.	O
,	O
because	O
the	O
output	O
exits	O
from	O
a	O
chain	O
of	O
integrators	O
,	O
every	O
state	O
has	O
an	O
effect	O
on	O
the	O
output	O
)	O
.	O
</s>
<s>
If	O
we	O
have	O
an	O
input	O
,	O
an	O
output	O
,	O
and	O
a	O
weighting	O
pattern	O
then	O
a	O
realization	B-Application
is	O
any	O
triple	O
of	O
matrices	B-Architecture
such	O
that	O
where	O
is	O
the	O
state-transition	O
matrix	O
associated	O
with	O
the	O
realization	B-Application
.	O
</s>
<s>
System	O
identification	O
techniques	O
take	O
the	O
experimental	O
data	O
from	O
a	O
system	O
and	O
output	O
a	O
realization	B-Application
.	O
</s>
<s>
eigensystem	O
realization	B-Application
algorithm	O
)	O
or	O
can	O
only	O
include	O
the	O
output	O
data	O
(	O
e.g.	O
</s>
