Robust fuzzy Lyapunov stabilization for uncertain and disturbed Takagi–Sugeno descriptors

In this paper, new robust H ∞ controller design methodologies for Takagi–Sugeno (T–S) descriptors is considered. Based on Linear Matrix Inequalities, two different approaches are proposed. The first one involves a “classical closed-loop dynamics” formulation and the second one a “redundancy closed-loop dynamics” approach. The provided conditions are obtained through a fuzzy Lyapunov function candidate and a non-PDC control law. Both the classical and redundancy approaches are compared. It is shown that the latter leads to less conservative stability conditions. The efficiency of the proposed robust control approaches for T–S descriptors as well as the benefit of the redundancy approach are shown through an academic example. Then, to show the applicability of the proposed approaches, the benchmark stabilization of an inverted pendulum on a cart is considered.