Why does the STABSEP function in the Control System Toolbox 6.2 (R14SP2) give incorrect results?

I use the STABSEP function on a system "sys" to decompose it into its stable and unstable parts. If the system "sys" is stable, I expect that the unstable part received on the execution of the STABSEP will be 0. However, I observe that the STABSEP function gives a non-zero unstable part, which is incorrect.

pole(sys);

[syss, sysus] = stabsep(sys);

Answer 1

[MathWorks Support Team]

This enhancement has been incorporated in Release 2006b (R2006b). For previous product releases, read below for any possible workarounds:

This enhancement has been incorporated in Release 2006a (R2006a). For previous product releases, read below for any possible workarounds:

This issue has been addressed by the new scaling algorithms in Control System Toolbox 7.0 (R2006a). If you are using a previous version, read the following:

There are some numerical difficulties in the Control System Toolbox 6.2 (R14SP2) in the way the STABSEP function handles systems with poles spread over a wide range.

As a workaround you can use

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) %create a system sys

[syss, sysus] = stabsep(ssbal(sys)); % performs full balancing of sys.a

instead of

[syss, sysus] = stabsep(sys);

where “sys” is the LTI model you want to decompose into its stable and unstable parts.