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 1.1 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); i = 0; for t = T' i=i+1; if Nx>0 expAt = expm(A*t); x = ( A\(expAt-one) )*B*u0 + expAt*x0; 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;