File: specfact.cat

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specfact(1)                    Scilab Function                    specfact(1)
NAME
  specfact - spectral factor

CALLING SEQUENCE
  [W0,L]=specfact(A,B,C,D)

DESCRIPTION
  Given a spectral density matrix phi(s):
                   -1                   -1
       R + C*(s*I-A) * B  +  B'*(-s*I-A') * C'  with R=D+D' > 0
  specfact computes  W0 and L such that  W(s)=W0+L*(s*I-A)^-1*B  is a spec-
  tral factor of of PHI(s), i.e.

  phi(s)=W'(-s)*W(s)

EXAMPLE
  A=diag([-1,-2]);B=[1;1];C=[1,1];D=1;s=poly(0,'s');
  W1=syslin('c',A,B,C,D);
  phi=gtild(W1,'c')+W1;
  phis=clean(ss2tf(phi))
  clean(phis-horner(phis,-s)');   //check this is 0...
  [A,B,C,D]=abcd(W1);
  [W0,L]=specfact(A,B,C,D);
  W=syslin('c',A,B,L,W0)
  Ws=ss2tf(W);
  horner(Ws,-s)*Ws

SEE ALSO
  gtild, sfact, fspecg

AUTHOR
  F. D.