Specifications

3 Operations on LTI Models
3-14
•Left division sys1\sys2, which is equivalent to inv(sys1)*sys2
•Right division sys1/sys2, which is equivalent to sys1*inv(sys2)
For a state-space model sys with data , inv(sys) is defined only
when is a square invertible matrix, in which case its state-space data is
Transposition
You can transpose an LTI model sys using
sys.'
This is a literal operation with the following effect:
•For TF models (with input arguments,
num and den), the cell arrays num and
den are transposed.
•For ZPK models (with input arguments,
z, p,andk), the cell arrays, z and p,
and the matrix
k are transposed.
•For SS models (with model data ), transposition produces the
state-space model A
T
, C
T
,B
T
,D
T
.
•For FRD models (with complex frequency response matrix
Response), the
matrix of frequency response data at each frequency is transposed.
Pertransposition
For a continuous-time system with transfer function , the pertransposed
system has the transfer function
The discrete-time counterpart is
Pertransposition of an LTI model
sys is performed using
sys'
You can use pertransposition to obtain the Hermitian (conjugate) transpose of
the frequency response of a given system. The frequency response of the
ABCD
,,,
D
ABD
1–
C ,– BD
1–
, D–
1–
C , D
1–
ABCD
,,,
Hs
()
Gs
()
Hs–
()[]
T
=
Gz
()
Hz
1–
()[]
T
=