In perturbation -based extremum-seeking methods, an excitation signal is added to the input, and the gradient, computed from the correlation between the input and output variations, is forced to zero. The main drawback of the method is that the speed of convergence, which is linked to the dither frequency, is slow due to the low value of dither frequency typically chosen. Increasing the excitation frequency may cause instability, but that could be corrected by phase compensation. In this paper, it is shown that an additional problem exists, i.e., the distance between the optimum and solution reached by the perturbation method is proportional to the square of the frequency of excitation and does not go to zero even when the amplitude of the excitation goes to zero. However, for Wiener/ Ham merstei n approximations, the error will indeed go to zero with the excitation amplitude. Simulation results on a distributed reaction system are used to illustrate the concepts presented in this work.