gram

Syntax

W = gram(SYS, 'c')

W = gram(SYS, 'o')

Inputs

SYS

A stable state-space model.

'o' or 'c'

A character.

'c'

Controllability.

'o'

Observability.

Outputs

W

The Gramian of the state-space model.

Example

a = [-1 0 0; 1/2 -1 0; 1/2 0 -1];
b = [1 0; 0 -1; 0 1];
c = [0 0 1; 1 1 0];
sys = ss (a, b, c,[]);
Wc = gram (sys, 'c')
Wo = gram (sys, 'o')

Wc = [Matrix] 3 x 3
0.50000   0.12500   0.12500
0.12500   0.56250  -0.43750
0.12500  -0.43750   0.56250
Wo = [Matrix] 3 x 3
0.87500  0.62500  0.12500
0.62500  0.50000  0.00000
0.12500  0.00000  0.50000

Comments

WC = gram(SYS, 'o') computes the observability Gramian of the state-space model SYS.

WC = gram(SYS, 'c') computes the controllability Gramian of the state-space model SYS.