Delay-dependent stability analysis and synthesis of uncertain T–S fuzzy systems with time-varying delay

This paper considers the delay-dependent stability analysis and controller design for uncertain T–S fuzzy system with time-varying delay. A new method is provided by introducing some free-weighting matrices and employing the lower bound of time-varying delay. Based on the Lyapunov–Krasovskii functio...

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Bibliographic Details
Published in:Fuzzy sets and systems 2006-02, Vol.157 (4), p.544-559
Main Authors: Tian, Engang, Peng, Chen
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Delay-dependent
Exact sciences and technology
Linear matrix inequality (LMI)
Mathematics
Nonlinear systems
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
System theory
T–S fuzzy systems
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Summary:This paper considers the delay-dependent stability analysis and controller design for uncertain T–S fuzzy system with time-varying delay. A new method is provided by introducing some free-weighting matrices and employing the lower bound of time-varying delay. Based on the Lyapunov–Krasovskii functional method, sufficient condition for the asymptotical stability of the system is obtained. By constructing the Lyapunov–Krasovskii functional appropriately, we can avoid the supplementary requirement that the time-derivative of time-varying delay must be smaller than one. The fuzzy state feedback gain is derived through the numerical solution of a set of linear matrix inequalities (LMIs). The upper bound of time-delay can be obtained by using convex optimization such that the system can be stabilized for all time-delays. The efficiency of our method is demonstrated by two numerical examples.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2005.06.022