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Stability analysis for discrete‐time fuzzy system by utilizing homogeneous polynomial matrix function
Author(s) -
Wang Likui,
Liu Xiaodong
Publication year - 2009
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.152
Subject(s) - homogeneous polynomial , degree (music) , lyapunov function , mathematics , polynomial , stability (learning theory) , control theory (sociology) , function (biology) , matrix (chemical analysis) , homogeneous , quadratic equation , fuzzy control system , fuzzy logic , nonlinear system , quadratic function , compensation (psychology) , computer science , control (management) , matrix polynomial , mathematical analysis , artificial intelligence , materials science , psychoanalysis , acoustics , composite material , biology , psychology , geometry , quantum mechanics , machine learning , evolutionary biology , physics , combinatorics
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. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society