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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.
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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
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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;
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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;
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