Switched Control for Local Stabilization of Discrete-time Uncertain Takagi-Sugeno Fuzzy Systems with Relaxed Estimate of the Domain of Attraction - Santos, Gilberto R. dos (2020)
This paper addresses the local stabilization problem and the computation of invariant subsets of the domain of attraction for uncertain nonlinear discrete-time systems. The proposed procedures use Takagi-Sugeno (T-S) fuzzy models that have uncertain membership functions and known local linear models. Based on a non-quadratic Lyapunov function, the proposed method uses a switched control law and the design conditions are given in terms of a optimization problem subject to Linear Matrix Inequalities (LMIs) constraints. The procedure provides a new and effective way to enlarge the estimation of the domain of attraction (DOA). Finally, a numerical example illustrates the effectiveness of the proposed method and compares it with procedures found in the literature.