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 we use a state transformation and choose a suitable Lyapunov function for the transformed control system. Using the Lyapunov function we estimate the ASR and show the exponential stability of the closed-loop control system in the region. Also, by an example we show that for a certain class of uncertain dynamical systems with bounded sliding mode controllers our method gives a more improved estimate of the ASR.