Generalized feedback interconnection of two models (Redheffer star product)
lft
sys = lft(sys1,sys2,nu,ny)
lft
forms the star product or linear fractional transformation (LFT) of
two model objects or model arrays. Such interconnections are widely
used in robust control techniques.
sys = lft(sys1,sys2,nu,ny)
forms the star product sys
of the two models (or
arrays) sys1
and sys2
. The star
product amounts to the following feedback connection for single models
(or for each model in an array).
This feedback loop connects the first nu
outputs
of sys2
to the last nu
inputs
of sys1
(signals u), and the
last ny
outputs of sys1
to the
first ny
inputs of sys2
(signals y).
The resulting system sys
maps the input vector
[w1 ; w2]
to the output vector [z1 ; z2].
The abbreviated syntax
sys = lft(sys1,sys2)
produces:
The lower LFT of sys1
and sys2
if sys2
has
fewer inputs and outputs than sys1
. This amounts
to deleting w2 and z2 in
the above diagram.
The upper LFT of sys1
and sys2
if sys1
has
fewer inputs and outputs than sys2
. This amounts
to deleting w1 and z1 in
the above diagram.
There should be no algebraic loop in the feedback connection.
The closed-loop model is derived by elementary state-space manipulations.