On the uncertain variable structure systems with bounded controllers

In this paper, we propose a method to estimate the asymptotic stability region (ASR) of uncertain variable structure systems with bounded controllers. Using linear matrix inequalities (LMIs) we estimate the ASR and we show the exponential stability of the closed-loop control system in the estimated ASR. We also give simple LMI-based algorithms for estimating the ASR and designing a switching surface which will make the estimated ASR big. Finally, we give numerical examples in order to show that our method can be better than the previous results for a certain class of uncertain variable structure systems with bounded controllers.