prescale

Descriptor state space model input:

A = [ -1       0       0  0.003;
       0       0  0.1000   0.02;
     100      10       0   0.4;
       0       0       0   0.0];

B = [   10         0;
         0         0;
         0      1000;
     10000     10000];

C = [ -0.1      0.0    0.001    0.0;
       0.0      0.01  -0.001    0.0001];

D = [];
E = [  1     0.2       0    0.0;
       0       1       0    0.01;
     300      90       6    0.3;
       0       0      20    0.0];

sysIn = dss (A, B, C, D, E);
[sysOut, info] = prescale(sysIn)

sysOut = object [
Scaled: 0
TimeUnit: seconds
ts: 0
a: [Matrix] 4 x 4
-1.00000  0.00000  0.00000  0.30000
 0.00000  0.00000  1.00000  2.00000
 1.00000  0.10000  0.00000  0.40000
 0.00000  0.00000  0.00000  0.00000
b: [Matrix] 4 x 2
100    0
  0    0
  0  100
100  100
c: [Matrix] 2 x 4
-0.01000  0.00000   0.00100  0.00000
 0.00000  0.00100  -0.00100  0.00100
d: [Matrix] 2 x 2
0  0
0  0
e: [Matrix] 4 x 4
1.00000  0.20000  0.00000  0.00000
0.00000  1.00000  0.00000  1.00000
3.00000  0.90000  0.60000  0.30000
0.00000  0.00000  0.20000  0.00000
type: StateSpaceModel
]
info = object [
SL: [Matrix] 4 x 1
10.00000
10.00000
 0.10000
 0.01000
SR: [Matrix] 4 x 1
 0.10000
 0.10000
 1.00000
10.00000
]

State space model input:

sys_tf = tf([1],[2 9 1]);
sysIn = ss(sys_tf);
[sysOut, info] = prescale(sysIn)

sysOut = object [
Scaled: 0
TimeUnit: seconds
ts: 0
a: [Matrix] 2 x 2
-4.50000  -0.50000
 1.00000   0.00000
b: [Matrix] 2 x 1
0.50000
0.00000
c: [Matrix] 1 x 2
0  1
d: 0
e: [Matrix] 0 x 0
type: StateSpaceModel
]
info = object [
SL: [Matrix] 2 x 1
1
1
SR: [Matrix] 2 x 1
1
1
]

INFO is a struct with two fields:

SL

Left scaling factors.

SR

Right scaling factors.

The scaling is performed with the following equations:

• As = Tl * A * Tr
• Bs = Tl * B
• Cs = C * Tr
• Ds = D
• Es = Tl * E * Tr
• Tl = diag(info.SL)
• Tr = diag(info.SR)