pfss

Name

pfss — partial fraction decomposition

Calling Sequence

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

Parameters

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)

Authors

F.D.;