Fuzzy dynamic output feedback control through nonlinear Takagi–Sugeno models

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.