y02ox.m

A Matlab toolbox for exact linear time-invariant system identification is presented. The emphasis is

% Y02OX - From a matrix of (sequential) free responses to an  
%         extended observability matrix (and a state sequence).
%
% [O,X] = y02ox(y0,n,tol)
%
% Y0 - matrix of (sequential) free responses 
%      (Y0(:,i) is a free response)
% LMAX - upper bound on the system lag
% N - optional order of the system
% TOL - tolerance for order selection, default 1e-7
%   If TOL < 0, the SVs are plotted and an input is asked.
% O - extended observability matrix
% X - state sequence

function [O,X] = y02ox(y0,n,tol)

% SVD of the matrix of (sequential) free responses 
[U,S,V] = svd(y0,0);
s = diag(S);

% if not given, determine the order
if (nargin < 3 | isempty(tol))
  tol = [];
end
if (nargin < 2 | isempty(n))
  n = order(s,tol);
end

% Rank revealing factorization
sqrt_s = sqrt(1./s(1:n))';
O = sqrt_s(ones(size(U,1),1),:) .* U(:,1:n);
if nargout > 1
  X = (sqrt_s(ones(size(V,1),1),:) .* V(:,1:n))';
end