Comments on "adaptive variable structure set-point control of underactuated robots"

Abstract

Recently, an adaptive variable structure controller was proposed in the above note1 to solve the set-point problem for underactuated robots. Specifically, a time-varying gain, denoted by k(t) 2 , was utilized in the control development and stability analysis which was generated via a discontinuous differential equation. Unfortunately, due to the discontinuous nature of the time derivative of k(t), erroneous arguments were utilized in the stability analysis which yield unexpected stability results. To illustrate that the stability arguments are invalid, we propose the following counter example