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# ss2tf

conversion from state-space to transfer function

### Syntax

```h = ss2tf(sl)
h = ss2tf(sl,"b")
h = ss2tf(sl,rmax)
[Ds, NUM, chi] = ss2tf(..)```

### Arguments

sl

linear system (`syslin` list)

h

transfer matrix

### Description

Called with three outputs `[Ds,NUM,chi]=ss2tf(sl)` returns the numerator polynomial matrix `NUM`, the characteristic polynomial `chi` and the polynomial part `Ds` separately i.e.:

`h = NUM/chi + Ds`

Method:

One uses the characteristic polynomial and `det(A+Eij)=det(A)+C(i,j)` where `C` is the adjugate matrix of `A`.

With `rmax` or `"b"` argument uses a block diagonalization of sl.A matrix and applies "Leverrier" algorithm on blocks. If given, `rmax` controls the conditioning (see bdiag).

### Examples

```s=poly(0,'s');
h=[1,1/s;1/(s^2+1),s/(s^2-2)]
sl=tf2ss(h);
h=clean(ss2tf(sl))
[Ds,NUM,chi]=ss2tf(sl)```

• tf2ss — transfer to state-space
• syslin — definição de sistemas lineares
• nlev — algoritmo de Leverrier
• glever — inverso do feixe de matrizes