conhsv.m

剑桥大学用于线性和双线性动力学系统辨识的工具箱

function t = conhsv(s,method)
%CONHSV   Convert distinct Hankel singular values into estimates.
%
%   T = CONHSV(S,METHOD) converts the distinct Hankel singular values S into
%   estimates T in order to remove the explicit constraints that they be
%   strictly positive and distinct, bearing in mind which METHOD will be
%   used to identify the system. The singular values have to be arranged
%   from the largest S(1) to the smallest S(end). If METHOD is 'ncf' or
%   'pr', then the singular values must also be strictly less than 1. The
%   singular values can be recovered by calling S = EXTHSV(T,METHOD).
%
%   See also EXTHSV.
%
% CUED System Identification Toolbox.
% Cambridge University Engineering Department.
% Copyright (C) 1998-2002. All Rights Reserved.

% Version 1.00, Date: 01/06/2002
% Created by H. Chen and E.C. Kerrigan.

if ~all(s > 0)
  error('Hankel singular values are not strictly positive.')
end

n = length(s);
t = s;

for i=1:n-1
  t(i) = s(i) - s(i+1);
end

if any(t == 0)
  error('Hankel singular values are not distinct.')
end  

if ~all(t > 0)
  error('Hankel singular values are not arranged from largest to smallest.')
end


switch method
 case{'sb','mp'}
  
   % This operation is the reverse of
   %     t = exp(t); 
   %     s = t; 
   %     for i=n-1:-1:1
   %       s(i) = t(i) + s(i+1); 
   %    end    

   t = log(t);
   
 case {'ncf','pr'}
  
  if ~all(s < 1)
	error('Hankel singular values are not strictly less than 1.')
  end
  
  % This operation is the reverse of
  %     s = t(:);
  %     s(1) = exp(t(1))/(1+exp(t(1)));
  %     for i=2:n
  %	      s(i) = s(i-1) * exp(t(i))/(1+exp(t(i)));
  %     end
  
  t(1) = log(s(1)/(1-s(1)));
  for i=2:n
	t(i) = log(s(i)/(s(i-1)-s(i)));
  end
 otherwise
  error('Unknown METHOD.')
end

t = t(:); % Vectorize