Fuzzy dynamic output feedback control through nonlinear Takagi–Sugeno models

• Published in: Fuzzy sets and systems Vol. 263; pp. 92 - 111
• Main Authors: Klug, Michael, Castelan, Eugênio B., Leite, Valter J.S., Silva, Luís F.P.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15-03-2015
• Subjects: Compensators; Control signal saturation; Design engineering; Dynamical systems; Fuzzy; Fuzzy anti-windup gain; Fuzzy logic; Fuzzy Lyapunov function; Fuzzy set theory; Local stability; Mathematical models; Nonlinear dynamics; Nonlinear Takagi–Sugeno models; Nonlinearity; Output feedback; Control signal saturation; Fuzzy anti-windup gain; Nonlinear Takagi–Sugeno models; Fuzzy Lyapunov function; Local stability; Output feedback
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2014.05.019

We present a convex way to design a fuzzy dynamic output feedback compensator for locally stabilizing a class of nonlinear discrete-time systems. This class consists of the systems described by Takagi–Sugeno (T–S) models with a sector bounded nonlinear additive term and saturated control signals. The local stabilization takes into account the domain of validity of these T–S models, which is a key issue for practical applications. Two types of nonlinear fuzzy compensators are considered, one having all matrices of the controller depending on fuzzy-grade membership functions and the other with only a subset of the matrices with such a dependency. The controller design includes a fuzzy anti-windup gain that handles saturating actuators. Besides, a time-performance index based on the λ-contractivity of the level set of the fuzzy Lyapunov function is proposed regarding the closed-loop system. Examples are given to illustrate the effectiveness of this proposal.