Delayed nonquadratic L2-stabilization of continuous-time nonlinear Takagi–Sugeno fuzzy models

• Published in: Information sciences Vol. 563; pp. 59 - 69
• Main Authors: Araújo, Rodrigo F., Coutinho, Pedro H.S., Nguyen, Anh-Tu, Palhares, Reinaldo M.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.07.2021
• Subjects: Fuzzy control; Nonlinear local models; Nonquadratic Lyapunov functions; Robust control; Takagi–Sugeno fuzzy models; Robust control; Fuzzy control; Nonquadratic Lyapunov functions; Nonlinear local models; Takagi–Sugeno fuzzy models
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2021.01.007

This work deals with the design of fuzzy controllers for stabilization of continuous-time nonlinear systems subject to L2 disturbances, which are represented by nonlinear Takagi–Sugeno fuzzy models, i.e., Takagi–Sugeno fuzzy models with nonlinear consequents. A nonquadratic Lyapunov function is used to derive sufficient design conditions based on linear matrix inequality constraints as well as to reduce the conservativeness when compared to existing control approaches in the literature. Furthermore, the nonquadratic Lyapunov function is defined in terms of an integral membership function, which leads to a delayed nonquadratic L2-stabilization condition. This condition avoids the well-known difficulties in dealing with time derivatives of membership functions and/or path-independent conditions, found in most of the nonquadratic control approaches for continuous-time Takagi–Sugeno fuzzy models. Two numerical examples are performed to illustrate the reduction in conservativeness provided by the proposed approach.