On delay-fractional-dependent stability criteria for Takagi-Sugeno fuzzy systems with interval delay
type: Item
instance of: scholarly article
title: On delay-fractional-dependent stability criteria for Takagi-Sugeno fuzzy systems with interval delay
zbMATH Open document ID: 1407.93207
DOI: 10.1155/2014/370382
author: Xianzhong Xia
author: Renfa Li
author: Jiyao An
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: This paper investigates stability program of Takagi-Sugeno fuzzy systems with interval time-varying delay via a variable delay decomposition approach. By developing a delay decomposition approach, both lower and upper bound information of the delayed plant states can be taken into full consideration; two novel delay-fractional-dependent stability criteria are obtained based on the direct Lyapunov method allied with an appropriate and variable Lyapunov-Krasovskii functional choice and with two different bounding techniques to estimate some integral terms in the time-derivative of the Lyapunov-Krasovskii functional. The first stability criterion is derived by utilizing the suitable and generalized integral inequalities, while the second stability condition is obtained by employing a scalar inequality, without any direct approximation. Particularly, the proposed results differ from previous ones since the positiveness of the Lyapunov-Krasovskii functional is guaranteed by new relaxed conditions. When applying these two stability criteria to check the stability of a T-S fuzzy system, it is shown through some numerical examples that the first stability condition can provide a larger maximum allowable delay bound than the second stability criterion, and both stability criteria yield less conservative than the existing ones.
Mathematics Subject Classification ID: 93C42
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K36
zbMATH DE Number: 7016281
Wikidata QID: Q59064727
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/370382
OpenAlex ID: W2035698914
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description: scientific article; zbMATH DE number 7016281