I want to simulate with various input.

As a general approach, you can compute the impulse response of the product of the transfer function and the input.

H = tf(1,[1 1]);  % assuming typo in the original question.
U1 = tf(1,[1 0]);
U2 = tf(1,[1 0],'InputDelay',2);

t = 0:.001:10;
y = impulse(H*(U1 - U2),t);

figure;plot(t,y),grid

In your particular case, the output is the difference between the step response and the step response delayed by t=2:

% assumes that any(t==2) is true
y1 = step(H,t);
y2 = 0*y1;
ii = find(t>=2);
y2(t>=2) = y1(1:length(ii));

figure;plot(t,y,t,y1-y2,'x'),grid