2017 journal article

Dynamic Output Feedback Control for Continuous-Time T-S Fuzzy Systems Using Fuzzy Lyapunov Functions

IEEE TRANSACTIONS ON FUZZY SYSTEMS, 25(5), 1155–1167.

By: Y. Liu, F. Wu n & X. Ban*

co-author countries: China 🇨🇳 United States of America 🇺🇸
author keywords: Continuous-time Takagi-Sugeno (T-S) fuzzy systems; full-block S-procedure; fuzzy Lyapunov functions; linear fractional transformation; output feedback control; relaxation method
Source: Web Of Science
Added: August 6, 2018

A novel relaxation approach is proposed for the analysis and dynamic output feedback control of continuous-time Takagi–Sugeno (T–S) fuzzy systems using fuzzy Lyapunov functions. Previous relaxation methods for T–S fuzzy systems have some drawbacks in relaxing quadratic functions depending on normalized fuzzy weighting functions. They often introduce conservatism or lead to computational difficulty in analysis and control synthesis. Different from previous works, the proposed approach employs linear fractional transformation mechanism and full-block <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S$</tex-math></inline-formula> -procedure to reduce the conservatism in analysis. Furthermore, the relaxation technique proposed in this paper can be used in solving the controller synthesis problem effectively. As a result, a design procedure of a nonparallel distributed compensation output feedback controller, which ensures asymptotic stability and optimizes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal L}_2$</tex-math></inline-formula> gain performance of the closed-loop systems, is provided. Several examples have been used to illustrate the advantages and efficiency of the proposed method extensively.