You do it for vectors pretty much the same way you would do it for scalars. The main difference would be that you need to account for the fact that x is a vector if you are saving all of the intermediate results. E.g., something like this:
% set constants etc here
x = some initial value
t = some initial value
dt = some step size
n = number of steps to take
xresult = zeros(numel(x),n); % allocate the result variable
xresult(:,1) = x; % save initial value
for k=2:n
% if needed, update A, B, U here
x_dot = A*x + B*U; % calculate derivative
x = x + x_dot*dt; % take the Euler step
t = t + dt;
xresult(:,k) = x; % save this intermediate result
end
