On the uncertain variable structure systems with bounded controllers (Q1398319)

Under suitable assumptions, the problem of estimating the asymptotic stability region (ASR) of uncertain variable structure systems with bounded controllers is studied. It is proved that there exists a sliding surface parameter matrix iff some linear matrix inequalities (LMI) hold true. Using these existence conditions, the problem of estimating the ASR is reduced to LMI optimization problems, and a LMI-based algorithm is proposed. These LMI optimization problems can be solved very efficiently. Thus one can easily design a switching surface which will make the estimated ASR big while guaranteeing the regional pole constraints of the sliding mode dynamics. Some numerical examples are also presented.