Stability analysis of delayed Takagi-Sugeno fuzzy systems: a new integral inequality approach

Volume 10, Issue 4, pp 1941--1959 http://dx.doi.org/10.22436/jnsa.010.04.53

Publication Date: April 20, 2017 Submission Date: November 17, 2016

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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.

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Keywords

• T-S fuzzy systems
• stability
• interval time-varying delay
• integral inequality
• Lyapunov-Krasovskii (LK) functional.

MSC

•  37B25
•  93C42
•  93D20

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