More precisely, in order to evaluate the controller performances, the IAE (integral of the absolute error) (or ISE: integral of the squared error) is generally used. Moreover, as well known in the HOSM theory, such controller is characterized by its sliding accuracy attained after the establishment of a real sliding motion (which mainly depend to the sampling time in the absence of noise and to the noise magnitude otherwise). The question is as follows: how can we interpret and discuss the tracking performance results provided by such HOSM controller using the both IAE criteria and SM accuracy in the same time?

In other hand, if we have different HOSM controllers (two SM-2 controllers for example), which provide the same IAE approximately but acheive a different order of sliding accuracies, how can we discuss this case?