Estimation of the asymptotic stability region of uncertain systems with bounded sliding mode controllers

In this note, the problem of estimating the asymptotic stability region (ASR) of uncertain systems with bounded sliding mode controllers is considered. To simplify the problem the authors use a state transformation and choose a suitable Lyapunov function for the transformed control system. Using the Lyapunov function the authors estimate the ASR and show the exponential stability of the closed-loop control system in the region. Also, by an example the authors show that for a certain class of uncertain dynamical systems with bounded sliding mode controllers their method gives a more improved estimate of the ASR