LFRT version 2.0: order reduction
This page describes two functions for order reduction after realization. Note that after realization, parameter commutativity is ignored (i.e., a*b-b*a connot be reduced to zero). Function minlfr1A system is defined, it will be used to illustrate the differences between both functions.
lfrs a b c d
sys1 = [a*c+a*d+b*c+b*d 1/(a*b*c);...
c+d 1/(a*b*c)];
size(sys1)
LFR-object with 2 output(s), 2 input(s) and 0 state(s).
Dimension of constant block in uncertainty matrix: 2
Uncertainty blocks (globally (16 x 16)):
Name Dims Type Real/Cplx Full/Scal Bounds
a 4x4 LTI r s [-1,1]
b 4x4 LTI r s [-1,1]
c 5x5 LTI r s [-1,1]
d 3x3 LTI r s [-1,1]
The function minlfr1 considers separately the parameters
for order reduction, so, the expected order reduction corresponds to the following
factorized from.
= [a+b 1/(a*b*c) ; 1 1/(a*b*c)] * ... [c+d 0 ; 0 1];i.e., order 10:
sys2 = minlfr1(sys1);
size(sys2)
LFR-object with 2 output(s), 2 input(s) and 0 state(s).
Dimension of constant block in uncertainty matrix: 2
Uncertainty blocks (globally (10 x 10)):
Name Dims Type Real/Cplx Full/Scal Bounds
a 3x3 LTI r s [-1,1]
b 3x3 LTI r s [-1,1]
c 3x3 LTI r s [-1,1]
d 1x1 LTI r s [-1,1]
Function minlfrThe function minlfr considers all parameters simultaneously for factorization, the expected order reduction corresponds to the following factorized form (considering the same system sys1 as above): = [a+b 1 ; 1 1] * ... [c+d 0 ; 0 1/(a*b*c)];i.e., order 7:
sys3 = minlfr(sys1);
size(sys3)
LFR-object with 2 output(s), 2 input(s) and 0 state(s).
Dimension of constant block in uncertainty matrix: 1
Uncertainty blocks (globally (7 x 7)):
Name Dims Type Real/Cplx Full/Scal Bounds
a 2x2 LTI r s [-1,1]
b 2x2 LTI r s [-1,1]
c 2x2 LTI r s [-1,1]
d 1x1 LTI r s [-1,1]
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