New stability conditions for uncertain T-S fuzzy systems with interval time-varying delay

This paper focuses on the stability problem for uncertain T-S fuzzy systems with interval time-varying delay. The system uncertainties are assumed to be time-varying and norm-bounded. The time-varying delay is considered as either being differentiable uniformly bounded with delay-derivative bounded...

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Bibliographic Details
Published in:International journal of control, automation, and systems 2012, Automation, and Systems, 10(3), , pp.490-497
Main Authors: An, Jiyao, Li, Tao, Wen, Guilin, Li, Renfa
Format: Article
Language:English
Subjects:
Analysis
Control
Control systems
Convex analysis
Delay
Derivatives
Engineering
Fuzzy systems
Interval arithmetic
Intervals
Laboratories
Linear programming
Lower bounds
Mechatronics
Optimization
Regular Papers
Robotics
Stability
Studies
제어계측공학
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Summary:This paper focuses on the stability problem for uncertain T-S fuzzy systems with interval time-varying delay. The system uncertainties are assumed to be time-varying and norm-bounded. The time-varying delay is considered as either being differentiable uniformly bounded with delay-derivative bounded by constant interval, or being fast-varying case with no restrictions on the delay derivative. Since we employ a novel Lyapunov-Krasovskii functional (LKF) which contains the information on the time-varying delay, and estimate the upper bound of its derivative less conservatively and adopt the convex optimization approach, some less conservative delay-derivative-dependent stability conditions are obtained in terms of linear matrix inequalities (LMIs), without using any free weighting matrix. These conditions are derived that depends on both the upper and lower bounds of the delay derivatives. Finally, some numerical examples are given to demonstrate the effectiveness and reduced conservatism of the proposed method.
ISSN:1598-6446
2005-4092
DOI:10.1007/s12555-012-0305-9