User`s guide

ssbal
11-216
11ssbal
Purpose Balance state-space models using a diagonal similarity transformation
Syntax [sysb,T] = ssbal(sys)
[sysb,T] = ssbal(sys,condT)
Description Given a state-space model sys with matrices ,
[sysb,T] = ssbal(sys)
computes a diagonal similarity transformation and a scalar such that
has approximately equal row and column norms.
ssbal returns the balanced
model
sysb with matrices
and the state transformation where is the new state.
[sysb,T] = ssbal(sys,condT) specifies an upper bound condT on the
condition number of . Since b alancing with ill-conditioned can
inadvertentlyma gnify roundingerrors,
condT givescontrolovertheworst-case
roundoff amplification factor. The default value is
condT=1/eps.
Example Consider the continuous-time state-space model with the following data.
a = [1 1e4 1e2;0 1e2 1e5;10 1 0];
b = [1;1;1];
c = [0.1 10 1e2];
sys = ss(a,b,c,0)
ABCD
,,,()
T
α
TAT
1–
TB α⁄
αCT
1–
0
TAT
1
–
TB α⁄αCT
1
–
D,,,()
xTx=
x
T
T
A
110
4
10
2
010
2
10
5
10 1 0
,= B
1
1
1
,= C
0.110100
=