LMI-Based Robust Adaptive Control for Mismatched Uncertain Nonlinear Time-Delay Systems Using Fuzzy Models

In this paper, we propose a robust adaptive control design method for uncertain fuzzy time-delay systems that can be represented by Takagi-Sugeno (T-S) fuzzy models. The uncertain fuzzy time-delay systems under consideration have mismatched parameter uncertainties in the state matrix and unknown norm-bounded 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 and an adaptation law so that a stable sliding motion is induced in finite time. Finally, we give a numerical example to show the effectiveness of the proposed method.