Function: fldown

sys = fldown(sys1,K)

Use of fldown and flup for mu-analysis. First, a random lfr-system and a random gain are generated:

   sys1 = rlfr(4,2,[-5 0;2 3;-2 0]);
   K = rss(3,2,4);

The feedback loop is closed using fldown. Note that lfr/feedback is similar to some extent, the main difference is that inputs and outputs disappear using fldown.

   sys2= fldown(sys1,K);
   size(sys1);

Lfr-object with 4 output(s), 2 input(s) and 5 state(s).
Uncertainty blocks (globally (4 x 5)).
  Block # 1 = full complex block  (2 x 3).
  Block # 2 = real parameter repeated 2 time(s).

   size(sys2);

Lfr-object with 0 output(s), 0 input(s) and 8 state(s).
Uncertainty blocks (globally (4 x 5)).
  Block # 1 = full complex block  (2 x 3).
  Block # 2 = real parameter repeated 2 time(s).

Computation of µ at 4.2 Rd/s

   sys3 = flup(sys2,[1/(4.2j);NaN;NaN]);
   size(sys3)

Lfr-object with 0 output(s), 0 input(s) and 0 state(s).
Uncertainty blocks (globally (4 x 5)).
  Block # 1 = full complex block  (2 x 3).
  Block # 2 = real parameter repeated 2 time(s).

   mubn = mu(sys3.a,[2 3;-2 0])

mubn =

    0.8844    0.8830

As a verification, let us use lfr2mua that performs fldown and flup internally.

   [sysmu,blkmu] = lfr2mua(sys1,4.2,K);
   mu(sysmu,blkmu)

mubn =

    0.8844    0.8830