function x = fltitr(a,b,u,x0,rules)
%  
% FLTITR  Linear time invariant time response
%
%         This function is designed to work similarly to the
%         Matlab internal function LTITR, however, it has
%         been externalized so that feedback control of the
%         input may be effected in a non-linear manner without
%         resorting to ODESIM routines.
%
%          Simulation performs the following:
%
%		 x[n+1] = Ax[n] + Bu[n]
%
%	to input sequence U. Matrix U must have as many columns as
%	there are inputs, u. Each row of U corresponds to a new
%	time point. FLTITR returns a matrix X with as many columns
%	as there are outputs y, and with LENGTH(U) rows.
% 
%       The string variable rules is the name of a function for 
%       use by FEVAL which will calculate U based on X.  For help 
%       construction of this function, see the demo file URUL1.M
%
%	FLTITR(A,B,U,X0) can be used if initial conditions exist.
%	Here is what it implements:
%
%		for i=1:n
%			x(:,i) = x0;
%    			x0 = a * x0 + b * RULES(u,x);
%		end
%		x = x.';

%	Roger McNichols   2/28/95

[n,m] = size(u);
  for i=1:n,
	x(:,i) = x0;

	x0 = a * x0 + b * feval(rules,u(i,:),x0);
  end
x = x.';