# Computing balanced representation for state-space model?

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Danijel Domazet on 2 Nov 2020
Answered: Ameer Hamza on 2 Nov 2020
I have the following state-space model parameters:
A = [0.989923894 -116924.375; 4.34027786e-10 1];
B = [1;0];
C = [0.010076086 1];
D = 0;
I would like to compute a balanced representation of this sistem using balreal():
[sysb,g,T,Ti] = balreal(sys)
How would I do that?
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### Answers (1)

Ameer Hamza on 2 Nov 2020
First create the ss() object
A = [0.989923894 -116924.375; 4.34027786e-10 1];
B = [1;0];
C = [0.010076086 1];
D = 0;
sys = ss(A, B, C, D);
[sysb,g,T,Ti] = balreal(sys)
Result
sysb =
A =
x1 x2
x1 0.995 -0.01599
x2 0.001586 0.995
B =
u1
x1 0.1157
x2 0.04721
C =
x1 x2
y1 0.07464 0.03044
D =
u1
y1 0
Continuous-time state-space model.
g =
Inf
Inf
T =
1.0e+05 *
0.0000 -3.9600
0.0000 9.7092
Ti =
7.4076 3.0213
-0.0000 0.0000
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