An efficient approach for reducing the conservatism of LMI-based stability conditions for continuous-time T–S fuzzy systems

This paper deals with reducing the conservatism of stability conditions for continuous-time T–S fuzzy systems. Previous stability conditions are relaxed by further exploring the properties of the time derivatives of normalized fuzzy weighting functions and by introducing more slack matrix variables....

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Bibliographic Details
Published in:Fuzzy sets and systems 2015-03, Vol.263, p.71-81
Main Authors: Xie, Xiang-Peng, Liu, Zhen-Wei, Zhu, Xun-Lin
Format: Article
Language:English
Subjects:
Continuous-time Takagi–Sugeno (T–S) fuzzy model
Derivatives
Design engineering
Fuzzy
Fuzzy logic
Fuzzy set theory
Fuzzy systems
Mathematical models
Slack variable technique
Stability
Stability analysis
Weighting functions
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Summary:This paper deals with reducing the conservatism of stability conditions for continuous-time T–S fuzzy systems. Previous stability conditions are relaxed by further exploring the properties of the time derivatives of normalized fuzzy weighting functions and by introducing more slack matrix variables. By relying on analysis of the positive and negative characteristics of the time derivatives of normalized fuzzy weighting functions, some redundant terms are removed from the problem formulation. Furthermore, more slack matrix variables are introduced to enlarge the design space. Consequently, less conservative stability conditions are obtained. Finally, a well-known numerical example is provided to illustrate the effectiveness of the proposed result.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2014.05.020