User`s guide

LTI Models
1-5
where each SISO entry is characterized by its n umerator and denominator.
Cell arrays provide an ide al means to specify the resulting arrays of
numeratorsanddenominators;see,“MIMOTransferFunctionModels”onpage
2-10 for more informati on. For example,
num = {0.5,[1 1]} % 1-by-2 cell array of numerators
den = {[1 0],[1 2]} % 1-by-2 cell array of denominators
H = tf(num,den)
creates the one-output/two-input transfer function
Alternatively, you c an create the same transfer function by matrix-like
concatenation of its SISO entries
h11 = tf(0.5,[1 0]) % 0.5/s
h12 = tf([1 1],[1 2]) % (s+1)/(s+2)
H = [h11,h12]
MIMO zero/pole/gain systems are defined in a similar fashion. For example,
the following commands specify above as a zero/pole/gain model
Zeros = {[],–1} % Note: use [] when no zero
Poles = {0 ,–2}
Gains = [0.5,1] % Note: use regular matrix for gains
H = zpk(Zeros,Poles,Gains)
Model Conversion
The functions tf, zpk, frd,andss also perform model conversion; see “Model
Conversion” on page 2-42 for more information. For example,
sys_ss = ss(sys)
converts some tf or zpk model sys to state space. Similarly, if you type
h = tf(1,[1 2 1]) % transfer function 1/(s^2+2s+1)
zpk(h)
Hs()
0.5
s
--------
s 1+
s 2+
------------
=
Hs
()