Robust adaptive controller design for uncertain fuzzy systems using linear matrix inequality approach

A robust adaptive control design method was developed for uncertain Takagi-Sugeno fuzzy models with norm-bounded uncertainties. We make the first attempt to relax the restrictive assumption that each nominal local system model shares the same input channel and the norm bound of the uncertainty is known, which is required in the traditional VSS-based fuzzy control design methods. We derive existence conditions of linear sliding surfaces guaranteeing the asymptotic stability in terms of constrained linear matrix inequalities (LMIs) and an LMI characterisation of such sliding surfaces is discussed. 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 two examples to show the effectiveness of the proposed method.