demo.m

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

% TEST the functions in the toolbox.

% ---- Simulation parameter
n = 5; m = 2; p = 3;

l = ceil(n/p);

lmax  = l;
nmax  = n;
delta = nmax+1;

s = 0;   % additive noise standard deviation
T = 500; % time horizon
L = 50;  % # of samples to be computed from the impulse response

% ---- Simulate impulse response
sys0 = drss_(n,p,m);
h0   = impulse(sys0,L);
if (m == 1)
  if (p > 1) 
    % transform the TxM H0 in PxMxT format
    h0s = h0; h0 = zeros(p,m,L);
    for t = 1:L
      h0(:,:,t) = h0s(t,:)';
    end
    clear h0s
  end
else
  h0  = shiftdim(h0,1);
end
ht   = randn(size(h0));
h    = h0 + s * ht;

% ---- Simulate input/output data
u0   = rand(T,m);
x0   = rand(n,1);
y0   = lsim(sys0,u0,[],x0);
ut   = randn(T,m);
yt   = randn(T,p);
u    = u0 + s * ut;
y    = y0 + s * yt;
w    = [u y];

% ---- Apply various (combinations of) functions

% UY2H
hh = uy2h(u,y,lmax,delta,L);
fprintf('%24s: error    = %f\n', 'uy2h', norm(h0(:)-hh(:)))

% UY2HBLK
hhblk = uy2hblk(u,y,lmax,L);
fprintf('%24s: error    = %f\n', 'uy2hblk', norm(h0(:)-hhblk(:)))

% UY2HY0
[hh,y0h] = uy2hy0(u,y,lmax,delta,L);
y0h_     = uy2y0(u,y,lmax,delta,L);
fprintf('%24s: error_h  = %f\n', 'uy2hy0', norm(h0(:)-hh(:)))
fprintf('%24s: error_y0 = %f\n', 'uy2hy0', norm(y0h(:)-y0h(:)))

% H2SS
sysh = h2ss(h);
fprintf('%24s: error    = %f\n', 'h2ss', norm(sys0-sysh,'inf'))

% UY2SSMR
sysh = uy2ssmr(u,y,lmax+1,n);
fprintf('%24s: error    = %f\n', 'uy2ssmr', norm(sys0-sysh,'inf'))

% UY2SSVD
sysh = uy2ssvd(u,y,lmax+1);
fprintf('%24s: error    = %f\n', 'uy2ssvd', norm(sys0-sysh,'inf'))

% UY2H -> H2SS
sysh  = uy2h2ss(u,y,lmax,delta);
fprintf('%24s: error    = %f\n', 'uy2h2ss', norm(sys0-sysh,'inf'))

% UY2Y0 -> Y02OX -> UYO2SS 
sysh  = uy2o2ss(u,y,lmax,delta);
fprintf('%24s: error    = %f\n', 'uy2o2ss', norm(sys0-sysh,'inf'))

% UY2Y0 -> Y02OX -> UYX2SS
sysh  = uy2x2ss(u,y,lmax,delta);
fprintf('%24s: error    = %f\n', 'uy2x2ss', norm(sys0-sysh,'inf'))

% UY2H -> H2OX -> UYO2SS 
sysh  = uy2h2o2ss(u,y,lmax,delta);
fprintf('%24s: error    = %f\n', 'uy2h2o2ss', norm(sys0-sysh,'inf'))

% UY2HY0 -> HY02OXBAL -> UYX2SS
sysh  = uy2ssbal(u,y,lmax,delta);
fprintf('%24s: error    = %f\n', 'uy2ssbal', norm(sys0-sysh,'inf'))

return

% W2R -> R2PQ -> PQ2SS
sysh  = w2r2ss([u,y],lmax);
fprintf('%24s: error    = %f\n', 'w2r2ss', norm(sys0-sysh,'inf'));