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Aide Scilab >> CACSD > pfss

pfss

partial fraction decomposition

Calling Sequence

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

Arguments

Sl

`syslin` list (state-space or transfer linear system) rmax : real number controlling the conditioning of block diagoanalization cord : character string `'c'` or `'d'`.

Description

Partial fraction decomposition of the linear system `Sl` (in state-space form, transfer matrices are automatically converted to state-space form by `tf2ss`):

`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 S according 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 and each subsystem `Si` is then converted in transfer form.

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`. If `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)```

See Also

• pbig — projection sur des sous-espaces propres
• bdiag — bloc-diagonalisation, vecteurs propres généralisés
• coffg — inverse d'une matrice de polynômes
• dtsi — stable anti-stable decomposition

F.D.;

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