Switched control for local stabilization of discrete-time uncertain takagi-sugeno fuzzy systems with relaxed estimate of the domain of attraction - Dos Santos, Gilberto R.; De Oliveira, Diogo R.; Teixeira, Marcelo C. M. [UNESP]; Assuncao, Edvaldo [UNESP]; Cardim, Rodrigo [UNESP]; Lazarini, Adalberto Z. N. [UNESP] (Institute of Electrical and Electronics Engineers (IEEE), 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.
Keywords: Discrete-time uncertain nonlinear system; Domain of attraction (DOA); Linear matrix inequality (LMI); Switched control; Takagi-Sugeno (T-S) fuzzy model; Uncertain membership functions