stabsep (Control System Toolbox)

Stable/unstable decomposition of LTI models

Syntax

[GS,GNS] = stabsep(G,CONDMAX)
[G1,G2] = STABSEP(G,CONDMAX,MODE,TOL)

Description

stapsep decomposes the LTI model into its stable and unstable parts

```
       G = GS + GNS
```

where GS contains all stable modes that can be separated from the unstable modes in a numerically stable way, and GNS contains the remaining modes. GNS is always strictly proper.

Use the optional input CONDMAX to control the condition number of the decoupling state transformation. Increasing CONDMAX helps separate close by stable and unstable modes at the expense of accuracy (see BDSCHUR for more details). By default CONDMAX=1e8.

[G1,G2] = STABSEP(G,CONDMAX,MODE,TOL) performs more general stable/unstable decompositions such that G1 includes all separable eigenvalues lying in one the following regions:

Table 0-7:
Mode
Continuous Time
Discrete Time

1
Re(s)<-TOL*max(1,|Im(s)|)
1 |z| < 1-TOL

2
Re(s)> TOL*max(1,|Im(s)|)

2 |z| > 1+TOL

**Table 0-7:**
Mode	Continuous Time	Discrete Time
`1`	`Re(s)<-TOL*max(1,\|Im(s)\|)`	`1 \|z\| < 1-TOL`
`2`	`Re(s)> TOL*max(1,\|Im(s)\|)`	`2 \|z\| > 1+TOL`

The default values are MODE=1 and TOL=0.

See Also
modsep Region-based modal decomposition

ssdata stack