Options for stable-unstable decomposition
opts = stabsepOptions
opts = stabsepOptions('OptionName', OptionValue)
opts = stabsepOptions returns the default options for the stabsep command.
opts = stabsepOptions('OptionName', OptionValue) accepts one or more comma-separated name/value pairs. Specify OptionName inside single quotes.
Focus of decomposition. Specified as one of the following values:
Absolute and relative error tolerance for stable/unstable decomposition. Positive scalar values. When decomposing a model G, stabsep ensures that the frequency responses of G and GS + GU differ by no more than AbsTol + RelTol*abs(G). Increasing these tolerances helps separate nearby stable and unstable modes at the expense of accuracy. See stabsep for more information.
Default: AbsTol = 0; RelTol = 1e-8
Offset for the stable/unstable boundary. Positive scalar value. The first output of stabsepincludes only poles satisfying:
Increase the value of Offset to treat poles close to the stability boundary as unstable.
For additional information on the options and how to use them, see the stabsep reference page.
Compute the stable/unstable decomposition of the system given by:
Use the Offset option to force stabsep to exclude the pole at s = 10–6 from the stable term of the stable/unstable decomposition.
G = zpk(-.5,[-1e-6 -2+5i -2-5i],10); opts = stabsepOptions('Offset',.001); % Create option set [G1,G2] = stabsep(G,opts) % treats -1e-6 as unstable
These commands return the result:
Zero/pole/gain: -0.17241 (s-54) --------------- (s^2 + 4s + 29) Zero/pole/gain: 0.17241 ---------- (s+1e-006)
The pole at s = 10–6 is in the second (unstable) output.