Indexed by:Journal Article

Date of Publication:2010-02-01

Journal:INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS

Included Journals:SCIE、EI

Volume:8

Issue:1

Page Number:118-126

ISSN:1598-6446

Key Words:Homogeneous polynomially basis-dependent matrix function; robust control; linear matrix inequality; non-quadratic Lyapunov function; Takagi-Sugeno's fuzzy model

Abstract:This paper studies the problem of robust H-infinity control for discrete-time nonlinear systems presented as Takagi-Sugeno's Fuzzy models. The generalized non-parallel distributed compensation (non-PDC) law and non-quadratic Lyapunov function is constructed by the proposed homogeneouspolynomially basis-dependent matrix function (HPB-MF for abbreviation). Based on the generalized non-PDC law and non-quadratic Lyapunov function, some linear matrix inequalities (LMIs) are obtained by exploiting the possible combinations of the basis functions. These LMIs ensure the asymptotic stability of the closed-loop system and guarantee a norm bound constraint on disturbance attenuation. In addition, it is shown that the LMIs become less conservative as the degree of HPB-MF increases. The merit of the methods presented in this paper lies in their less conservatism than other methods, as shown by a numerical example borrowed from the literature.