User`s guide

2 LTI Models
2-10
MIMO Transfer Function Models
MIMO transfer functions are two-dimensional arrays of elementary SISO
transfer f un c tio n s. There are se v era l ways t o specify MIM O transfer func tio n
models, including:
• Concatenation o f SISO transfer function models
• Using
tf with cell array arguments
Consider the rati onal transfer matrix
.
You can s p ecify by co nca te nati on of its SISO entries. Fo r ins tance ,
h11 = tf([1 –1],[1 1]);
h21 = tf([1 2],[1 4 5]);
or, equivalently,
s = tf('s')
h11 = (s–1)/(s+1);
h21 = (s+2)/(s^2+4*s+5);
can be concatenated to form .
H = [h11; h21]
This syntax mimics standard matrix concatenation and tends to be easier and
morereadablefor MIMOsystemswithmany inputs and/oroutputs.See“Model
Interconnection Functions” on page 3-16 for more details on concatenation
operations for LTI systems.
Alternatively, to define MIMO transfer functions using
tf, you need two cell
arrays (say,
N and D) to represent the sets of numerator and denominator
polynomials, respectively. See Chapter 13, “Structures and Cell Arrays” in
Using MATLAB for more details on cell arrays.
Hs()
s 1–
s 1+
------------
s 2+
s
2
4 s 5++
----------------------------
=
Hs
(
)
Hs
()