Check whether an LTI system is stable.
Description
This routine checks whether an LTI system is stable, i.e. whether all its eigenvalues are inside the left half plane or a given truncated sector.
Syntax
[stable,w]=check_stab(sys{,sector})Input arguments
sys | LTI object or square matrix whose stability has to be tested. A list of eigenvalues can also be directly given. |
sector | Vector $[\alpha\ \xi]$ or $[\alpha\ \xi\ \omega_c]$ characterizing the considered truncated sector (see display_sector for a complete description). This parameter is optional and the default value is sector=[0 0], which means that the left half plane is considered. |
Output arguments
stable | Boolean indicating whether sys is stable (1) or not (0). |
w | Imaginary part of the most unstable eigenvalue. |
Example
sys=rss(10,1,1);sys.a=sys.a-0.1*eye(10);[stable,w]=check_stab(sys)
All eigenvalues of sys are inside the left half plane, so stable is equal to 1 and w is empty.sys=[-1 -3 -1+2i -1-2i -2+3i -2-3i];sector=[-0.8 0.3 1];[stable,w]=check_stab(sys,sector)display_sector(sector,sys);
The eigenvalues $-1\pm 2i$ are outside the considered sector, so stable is equal to 0 and w is equal to 2.
See also