On Switched Regulator Design of Uncertain Nonlinear Systems Using Takagi-Sugeno Fuzzy Models

• Published in: IEEE transactions on fuzzy systems Vol. 22; no. 6; pp. 1720 - 1727
• Main Authors: de Souza, Wallysonn A., Teixeira, Marcelo C. M., Cardim, Rodrigo, Assuncao, Edvaldo
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-12-2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bilinear matrix inequalities (BMIs); control of uncertain nonlinear systems; Controllers; Design engineering; Fuzzy; Fuzzy logic; Fuzzy set theory; Indexes; linear matrix inequalities (LMIs); Lyapunov methods; Mathematical analysis; Mathematical models; Nonlinear systems; Nonlinearity; switched control; Switches; Symmetric matrices; Takagi-Sugeno (T-S) fuzzy model; Takagi-Sugeno model
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2014.2302494

This paper is concerned with the design of state-feedback switched controllers for a class of uncertain nonlinear plants described by Takagi-Sugeno (T-S) fuzzy models. The proposed methodology eliminates the need to find the membership function expressions to implement the control law, which is relevant in cases where the membership function depends on uncertain parameters. The design of the switched controllers is based on a minimum-type Lyapunov function and the minimization of the time derivative of this Lyapunov function. The conditions of the new stability criterion are represented by a kind of bilinear matrix inequalities (BMIs) that has been solved by the path-following method. A numerical example and the nonlinear control design of a magnetic levitator with uncertainties illustrate the procedure.