I don't think this problem is well suited for vectorization since you are already doing matrix multiplication at each iteration of the loop; however, you can get a very nice speedup by taking the expm call outside of the loop.
Using the property e^(aX) = (e^X)^a you can refactor your code to calculate
E = expm(AcT*delta_ksi);
before the loop and use
E^i
in place of
expm(AcT*delta_ksi*i)
in your loop.
Since you are calculating consecutive exponents, why not do the multiplication yourself for an extra speedup?
E0 = expm(AcT*delta_ksi);
E1 = eye(4);
% calculate the sum
for ii = 1:N
E1 = E0*E1;
Fl = E1*post*[wy1(1,ii); wy2(1,ii);];
sum_matrix = sum_matrix+Fl;
end
Bonus suggestion, ii makes a good loop variable name when you want something short because it doesn't conflict with the complex variable i.
