Robust sliding control for mismatched uncertain fuzzy time-delay systems using linear matrix inequality approach

Abstract

In this article, we propose a robust sliding control design method for uncertain time-delay systems that can be represented by Takagi–Sugeno fuzzy models. The uncertain fuzzy time-delay systems under consideration have mismatched parameter uncertainties in the state matrix and external disturbances. We derive existence conditions of linear sliding surfaces guaranteeing the asymptotic stability in terms of constrained linear matrix inequalities (LMIs). We present an LMI characterization of such sliding surfaces. Also, an LMI-based algorithm is given to design the switching feedback control term so that a stable sliding motion is induced in finite time. Finally, we give two numerical design examples to show the effectiveness of the proposed method.