Global asymptotical stability of a Logistic model with feedback control

The global asymptotical stability of the following Logistic equation with feedback control {dx(t)dt=x(t)[1−x(t)K−u(t)],du(t)dt=−ηu(t)+ax(t), is considered, where KK, ηη, aa are all positive constants. Here we use a new method combined with the upper and lower solution technique, which is more simple and convenient than the Lyapunov function method.