Specifications

2 LTI Models
2-12
Zero-Pole-Gain Models
This section explains how to specify continuous-time SISO and MIMO
zero-pole-gain models. The specification for discrete-time zero-pole-gain
models is a simple extension of the continuous-time case. See “Discrete-Time
Models” on page 2-19.
SISO Zero-Pole-Gain Models
Continuous-time SISO zero-pole-gain models are of the form
where is a real-valued scalar (the gain), and ,..., and ,..., are the
real or complex conjugate pairs of zeros and poles of the transfer function .
This model is closely related to the transfer function representation: the zeros
are simply the numerator roots, and the poles, the denominator roots.
There are two ways to specify SISO zero-pole-gain models:
•Using the
zpk command
•As rational expressions in the Laplace variable s
ThesyntaxtospecifyZPKmodelsdirectlyusing
zpk is
h = zpk(z,p,k)
where z and p are the vectors of zeros and poles, and k is the gain. This
produces a ZPK object
h that encapsulates the z, p,andk data. For example,
typing
h = zpk(0, [1–i 1+i 2], –2)
produces
Zero/pole/gain:
–2 s
--------------------
(s–2) (s^2 – 2s + 2)
You can also specify zero-pole-gain models as rational expressions in the
Laplace variable s by:
hs
()
k
sz
1
–
()
... sz
m
–
()
sp
1
–
()
... sp
n
–
()
-------------------------------------------------
=
kz
1
z
m
p
1
p
n
hs
()