frnmat.m

MFD－多变量系统频域设计工具

function [d,rsigma]=frnmat(w,f)
%FRNMAT	Calculates the normalized row dominance scalings.
%	FRNMAT(W,F) returns an MVFR matrix of real positive diagonal
%	pre-multiplier matrices which scale Fm so that the row
%	diagonal dominance of Fm*Dm 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,Rsigma]=FRNMAT(W,F) also returns the normalized row
%	sigmas in the column vector Rsigma.
%
%	To check the row dominance use
%	  plotdb(w,frdom(w,fmulf(w,f,d)))
%	The stability similarity transformation is    Dm^(-1) * Fm * Dm
%	  fmulf(w,finv(w,d),fmulf(w,f,d))
%
%	See also FCNMAT,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=[];
rsigma=[];
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))];
  rsigma=[rsigma;sigma];
end