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  ## xs          x*, one column for each time tau 
  ## xu          x_u, one column for each time tau 
  ## AA          The composite system matrix
  
  ## Copyright (C) 1999 by Peter J. Gawthrop
  ## 	$Id$	


  [n_x,n_u,n_y] = abcddim(A,B,C,D); # System dimensions
  if (size(A)>0)
    [n_x,n_u,n_y] = abcddim(A,B,C,D); # System dimensions
  else
    n_x = 0;
    n_y = 0;
    n_u = 0;
  endif
  
  no_system = n_x==0;

  [n,m] = size(A_u);		# Size of composite A_u matrix
  square = (n==m);		# Is A_u square?
  n_U = m;			# functions per input

  
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  n_xx = length(xx_0);		# Length of composite state

  ## Compute the star variables
  for t=tau
    xxt = expm(AA*t)*xx_0;	# Composite state
    xst = xxt(1:n_x);		# x star
    xut = xxt(n_x+1:n_xx);	# x star
    if length(C)>0
    yst = C*xst;		# y star
      yst = C*xst;		# y star
    else
      yst = [];
    endif
    
    ust = Utilde*xut;		# u star

    xs = [xs xst];		# x star
    xu = [xu xut];		# x star
    ys = [ys yst];		# y star
    us = [us ust];		# u star
  endfor

endfunction

MTT: Model Transformation Tools
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