Title of Paper:STABILITY ANALYSIS FOR DISCRETE-TIME FUZZY SYSTEM BY UTILIZING HOMOGENEOUS POLYNOMIAL MATRIX FUNCTION

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Date of Publication:2009-11-01

Journal:ASIAN JOURNAL OF CONTROL

Included Journals:SCIE、EI、Scopus

Volume:11

Issue:6

Page Number:700-706

ISSN No.:1561-8625

Key Words:Takagi-Sugeno's fuzzy model; homogeneous polynomial matrix function; non-quadratic Lyapunov function; parallel distributed compensation law; linear matrix inequality

Abstract:The purpose of this paper is to investigate the stability of nonlinear systems represented by a Takagi-Sugeno discrete-time fuzzy model. The homogeneous polynomial matrix function (HPMF) is developed to obtain new stabilization conditions. Applying the HPMF to the non-parallel distributed compensation (non-PDC) law and non-quadratic Lyapunov function, some new stabilization conditions are obtained by the following two means: (a) utilizing the popular idea of introducing additional variables for some fixed degree of the HPMF; and (b) increasing the degree of the HPMF. It is shown that the conditions obtained with approach (a) are less conservative than some sufficient stability conditions available in the literature to date. It is also shown that as the degree of HPMF increases the conditions obtained under (b) become less conservative. An example is provided to illustrate how the proposed approaches compare with other techniques available in the literature.