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# pfss

partial fraction decomposition

### Calling Sequence

```elts=pfss(Sl)
elts=pfss(Sl,rmax)
elts=pfss(Sl,cord)
elts=pfss(Sl,rmax,cord)```

### Arguments

Sl

A linear dynamical system in state-space or transfer function representation (see syslin).

rmax

A real number controlling the conditioning of block diagonalization (see bdiag).

cord

A character string with possible values `'c'` or `'d'`.

### Description

Partial fraction decomposition of the linear system `Sl`.

`elts` is the list of linear systems which add up to `Sl` i.e. `elts=list(S1,S2,S3,...,Sn)` with:

`Sl = S1 + S2 +... +Sn`.

Each `Si` contains some poles of Saccording to the block-diagonalization of the `A` matrix of `S`.

For non proper systems the polynomial part of `Sl` is put in the last entry of `elts`.

If `Sl` is given in transfer form, it is first converted into state-space by tf2ss and each subsystem `Si` is then converted in transfer form by ss2tf.

The A matrix is of the state-space is put into block diagonal form by function bdiag. The optional parameter `rmax` is sent to `bdiag`, `rmax` should be set to a large number to enforce block-diagonalization.

If the optional flag `cord='c'` is given the elements in `elts` are sorted according to the real part (resp. magnitude if `cord='d'`) of the eigenvalues of A matrices.

### Examples

```W=ssrand(1,1,6);
elts=pfss(W);
W1=0;for k=1:size(elts), W1=W1+ss2tf(elts(k));end
clean(ss2tf(W)-W1)```
```num=22801+4406.18*s+382.37*s^2+21.02*s^3+s^4;
den=22952.25+4117.77*s+490.63*s^2+33.06*s^3+s^4
h2=syslin('c',num/den);```

• pbig — autoprojeção
• bdiag — diagonalização em blocos, autovetores generalizados
• coffg — matriz inversa de polinômios
• dtsi — Continuous time dynamical systems stable anti-stable decomposition