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Routine check_stab

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

display_sector