I don't know how your DDE system is modeled, but you can probably try something like this to locate the position of the time stamp where Your Settling Time is defined.
k1 = 39.5;
k2 = 6.5;
F = @(t, x) [x(2); ...
- k1*x(1) - k2*x(2)];
x0 = [0.14, 0];
tspan = [0, 15];
[t, x] = ode45(F, tspan, x0);
plot(t, x(:,1), 'linewidth', 1.5), ylim([-0.05 0.15])
% Find index of time-stamp based on 2% criterion
index = find(t > 1 & x > -0.02*x0(1) & x < 0.02*x0(1));
position = index(1)
SettlingTime = t(position)
