Stability analysis of delayed Takagi-Sugeno fuzzy systems: a new integral inequality approach
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Authors
Jiyao An
- College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China.
Xinzhi Liu
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
Guilin Wen
- State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China.
Abstract
This paper is concerned with the problem of the stability analysis for Takagi-Sugeno (T-S) fuzzy systems with interval
time-varying delay. The delay is assumed to be differential with interval bounds, and has both the lower and upper bounds
of the delay derivatives, in which the upper bound of delay derivative may be greater than one. By constructing some delaydependent
Lyapunov functions, some stability criteria are derived by using the convex optimization method and new integral
inequality techniques. Utilizing integral inequalities for quadratic functions plays a key role in the field of stability analysis for
delayed T-S fuzzy systems, and some integral inequalities for quadratic functions are derived and employed in order to produce
tighter bounds than what the Jensen inequality and Wirtinger-based inequality produce. Then, less conservative stability criteria
are derived by using convex combination method and improved integral inequalities based on appropriate Lyapunov-Krasovskii
(LK) functional. Finally, several examples are given to show the advantages of the proposed results.
Share and Cite
ISRP Style
Jiyao An, Xinzhi Liu, Guilin Wen, Stability analysis of delayed Takagi-Sugeno fuzzy systems: a new integral inequality approach, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1941--1959
AMA Style
An Jiyao, Liu Xinzhi, Wen Guilin, Stability analysis of delayed Takagi-Sugeno fuzzy systems: a new integral inequality approach. J. Nonlinear Sci. Appl. (2017); 10(4):1941--1959
Chicago/Turabian Style
An, Jiyao, Liu, Xinzhi, Wen, Guilin. "Stability analysis of delayed Takagi-Sugeno fuzzy systems: a new integral inequality approach." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1941--1959
Keywords
- T-S fuzzy systems
- stability
- interval time-varying delay
- integral inequality
- Lyapunov-Krasovskii (LK) functional.
MSC
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