the LTI model
G into its stable and unstable parts
G = GS + GNS
GS contains all stable modes that can
be separated from the unstable modes in a numerically stable way,
GNS contains the remaining modes.
always strictly proper.
absolute and relative error tolerances for the stable/unstable decomposition.
The frequency responses of
GNS should differ by no more than
Increasing these tolerances helps separate nearby stable and unstable
modes at the expense of accuracy. The default values are
a more general stable/unstable decomposition where
all separable poles lying in the regions defined using offset
This can be useful when there are numerical accuracy issues. For example,
if you have a pair of poles close to, but slightly to the left of
the jω-axis, you can decide not to include
them in the stable part of the decomposition if numerical considerations
lead you to believe that the poles may be in fact unstable
This table lists the stable/unstable boundaries as defined by
Continuous Time Region
Discrete Time Region
The default values are
the stable/unstable decomposition of
G using the
options specified in the
Compute a stable/unstable decomposition with absolute error no larger than 1e-5 and an offset of 0.1:
h = zpk(1,[-2 -1 1 -0.001],0.1) [hs,hns] = stabsep(h,stabsepOptions('AbsTol',1e-5,'Offset',0.1));
The stable part of the decomposition has poles at -1 and -2.
hs Zero/pole/gain: -0.050075 (s+2.999) ------------------- (s+1) (s+2)
The unstable part of the decomposition has poles at +1 and -.001 (which is nominally stable).
hns Zero/pole/gain: 0.050075 (s-1) --------------- (s+0.001) (s-1)