function [Y,X] = sm2sr(A,B,C,D,T,u0,x0);
% [Y,X] = sm2sr(A,B,C,D,T,u0,x0);
% Constrained-state matrix to impulse response.
% 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 1.2 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;