fcnmat.m

MFD－多变量系统频域设计工具

function [d,csigma]=fcnmat(w,f)
%FCNMAT	Calculates the normalized column dominance scalings.
%	FCNMAT(W,F) returns an MVFR matrix of real positive diagonal
%	post-multiplier matrices which scale Fm so that the column
%	diagonal dominances of Dm*Fm are normalize to the same value.
%	Fm and Dm are the component matrices of F and D respectively.
%	W is the associated frequency vector.
%
%	[D,Csigma]=FCNMAT(W,F) also returns the normalized column
%	sigmas in the column vector Csigma.
%
%	To check the column dominance use
%	  plotdb(w,fcdom(w,fmulf(w,d,f)))
%	The stability similarity transformation is    Dm * Fm * Dm^(-1)
%	  fmulf(w,fmulf(w,d,f),finv(w,d))
%
%	See also FRNMAT,FRDOM,FCDOM

%	Dr M.P. Ford 22nd August 1987
% Copyright (c) 1987 by GEC Engineering Research Centre & Cambridge Control Ltd
%       MRN0019

[m,n]=fsize(w,f);
if m~=n
   error('System is not square')
end
f=abs(f);
lw=length(w);
k=1:m;
d=[];
csigma=[];
for i=0:lw-1
  fm=f(k+m*i,:);  % break up f into matrices
  fd=diag(fm);
  fm=fm-diag(fd);       %  make the diagonals zero
  fd=diag(fd.^(-1));    % make 1/diagonal
  [di,v]=eig(fd*(fm'));
  [sigma,i]=max(max(v));     % max eigenvalue
  if (sigma<=0) | any(di(:,i)<=0)
      error('System is not Irreducible')
  end
  d=[d;diag(di(:,i))];
  csigma=[csigma;sigma];
end