pfss

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);

See also

• pbig — eigen-projection
• bdiag — block diagonalization, generalized eigenvectors
• coffg — inverse of polynomial matrix
• dtsi — Continuous time dynamical systems stable anti-stable decomposition