function [Y,X] = sm2sr(A,B,C,D,T,u0,x0);
% sm2sr - Constrained-state matrix to step response.
%
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%     %%%%% Model Transformation Tools %%%%%
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% Matlab function  sm2sr
% [Y,X] = sm2sr(A,B,C,D,T,u0,x0);
% A,B,C,D,E - (constrained) state matrices
% T vector of time points
% u0 input gain vector: u = u0*unit step.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.3  1996/10/27  10:39:04  peterg
% %% Only compute matrix exponential once.
% %%
% %% Revision 1.2  1996/09/10  16:48:21  peter
% %% Changed ar counts in default settings.
% %%
% %% Revision 1.1  1996/08/19 15:34:29  peter
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


[Ny,Nu] = size(D);
[Ny,Nx] = size(C);

if nargin<6
  u0 = zeros(Nu,1);
  u0(1) = 1;
end;

if nargin<7
  x0 = zeros(Nx,1);
end;

[N,M] = size(T);
if M>N
  T = T';
  N = M;
end;



% $$$ one = eye(Nx);
% $$$ 
% $$$ Y = zeros(N,Ny);
% $$$ X = zeros(N,Nx);
% $$$ 
% $$$ dt = T(2)-T(1);% Assumes fixed interval
% $$$ expAdt = expm(A*dt); % Compute matrix exponential
% $$$ i = 0;
% $$$ expAt = one;
% $$$ 
% $$$ for t = T'
% $$$   i=i+1;
% $$$   if Nx>0
% $$$     x = ( A\(expAt-one) )*B*u0 + expAt*x0;
% $$$     expAt = expAt+expAdt;
% $$$     X(i,:) = x';
% $$$     if Ny>0
% $$$       y = C*x + D*u0;
% $$$       Y(i,:) = y';
% $$$     end;
% $$$   elseif Ny>0
% $$$     y = D*u0;
% $$$     Y(i,:) = y';
% $$$   end;
% $$$ end;

% Compute the impulse response
[Y,X] = sm2ir(A,B,C,D,T,u0,x0);

% Assume fixed sample interval
dT = T(2)-T(1);

% Do an Euler integration on it
 Y = mtt_euler(Y,dT);
 
 if nargout>1
   X = mtt_euler(X,dT);
 end;