52 Feedback Control in Systems Biology
Indeed, the latter has two r eal po les (ζ > 1), and thus exhibits a limited initial
overshoot, a fast initial rise (due to the pole with small time c onstant) and a
slow decay (caused by the large time consta nt assoc iated with the other real
pole).
The identified mode l can be translated into the state-space canonical form
˙x
1
˙x
2
=
0 −ω
2
n
1 −2ζω
n
x
1
x
2
+
0
Kω
2
n
u (2.46a)
y = x
2
(2.46b)
Since the second state variable coincides with the obser vable output of the
system, it ca n be readily associated with a physical quantity of the proce ss
(the level of Hog1 a ctivity), and thus it is convenient to leave it unchanged.
However, the hidden state variable x
1
can be arbitrarily substituted with a
new one, denoted by