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