Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems

Park, PooGyeon; Lee, Won Il; Lee, Seok-Young

doi:10.1016/j.jfranklin.2015.01.004

Cited by 708 publications

(302 citation statements)

References 23 publications

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“…Revisiting the literature [14,17,23,26], the most commonly used LKF consists of the following double and triple integral terms:…”

Section: New Integral Inequalitiesmentioning

confidence: 99%

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Improved Integral Inequalities for Stability Analysis of Interval Time-Delay Systems

Shuai

2017

Algorithms

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Abstract:A novel stability analysis for the interval time-delay systems is proposed by employing a new series of integral inequalities for single and double integrals. Different from the recently introduced Wirtinger-based inequalities, refined Jensen inequalities and auxiliary function-based inequalities, the proposed ones can provide more accurate bounds for the cross terms in derivatives of the Lyapunov-Krasovskii functional (LKF) without involving additional slack variables. Based on the augmented LKF with triple-integral terms, their applications to stability analysis for interval time-delay systems are provided. By virtue of the newly derived inequalities, the resulting criteria are less conservative than some existing literature. Finally, numerical examples are provided to verify the effectiveness and improvement of the proposed approaches.

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“…Revisiting the literature [14,17,23,26], the most commonly used LKF consists of the following double and triple integral terms:…”

Section: New Integral Inequalitiesmentioning

confidence: 99%

“…By the Wirtinger-based inequality [19], the new inequality [17] and the auxiliary function-based inequality [26] (the refined Jensen inequality [23]), respectively,…”

Section: Remarkmentioning

confidence: 99%

Improved Integral Inequalities for Stability Analysis of Interval Time-Delay Systems

Shuai

2017

Algorithms

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“…However, Jensen's like inequality inevitably introduces some undesirable conservatism. It has been improved by [13] which dealt with single integral and double integral terms. As a result, a new class of inequalities are presented, which produce tighter bounds than what the Jensen inequality produces in [13].…”

Section: Introductionmentioning

confidence: 99%

“…It has been improved by [13] which dealt with single integral and double integral terms. As a result, a new class of inequalities are presented, which produce tighter bounds than what the Jensen inequality produces in [13]. Very recently, a less conservative inequality was introduced based on the free-matrix ideal [21,22].…”

Section: Introductionmentioning

confidence: 99%

“…Very recently, a less conservative inequality was introduced based on the free-matrix ideal [21,22]. They provided a better condition on the single integral inequality than [13]. On the other hand, research on double integral inequality and triple integral inequality should not be ignored, because such inequalities may play an important role in obtaining delay-dependent stability condition for neutral delay systems.…”

Section: Introductionmentioning

confidence: 99%

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Improved conditions for neutral delay systems with novel inequalities

Xiong¹,

Cheng²,

Liu³

et al. 2017

J. Nonlinear Sci. Appl.

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This paper studies the stability problem of a class of neutral delay systems. It firstly establishes two novel integral inequalities, which are better than the same type inequalities found in the literature. Then it derives, by using the new inequalities and the Lyapunov functional method, some sufficient delay-dependent conditions for asymptotic stability of the neutral delay systems. Three numerical examples are provided to illustrate the advantage and effectiveness of the obtained results.

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Full and reduced‐order H_∞ filtering of Takagi–Sugeno fuzzy time‐varying delay systems: Input–output approach

Aiss

Zoulagh

Hmamed

2021

Adaptive Control & Signal

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Summary This article addresses the issue of delay‐dependent H∞ filtering design for TakagiŮSugeno fuzzy time‐varying delay systems using the input–output approach. A three‐term approximation model has been used to transform the original system into two interconnected subsystems. Since the nonquadratic Lyapunov–Krasovskii functional requires to deal with the membership function's (MF) time derivative, upper‐bound inequalities have been added to the obtained conditions. Based on the scaled small gain theorem, nonquadratic Lyapunov–Krasovskii functional approach and considering the bounds of the MF time‐derivative, the H∞ full‐ and reduced‐order filters are designed and then formulated in terms of linear matrix inequalities. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods.

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Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems

Cited by 708 publications

References 23 publications

Improved Integral Inequalities for Stability Analysis of Interval Time-Delay Systems

Improved Integral Inequalities for Stability Analysis of Interval Time-Delay Systems

Improved conditions for neutral delay systems with novel inequalities

Full and reduced‐order H_∞ filtering of Takagi–Sugeno fuzzy time‐varying delay systems: Input–output approach

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Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems

Cited by 708 publications

References 23 publications

Improved Integral Inequalities for Stability Analysis of Interval Time-Delay Systems

Improved Integral Inequalities for Stability Analysis of Interval Time-Delay Systems

Improved conditions for neutral delay systems with novel inequalities

Full and reduced‐order H∞ filtering of Takagi–Sugeno fuzzy time‐varying delay systems: Input–output approach

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Product

Resources

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Full and reduced‐order H_∞ filtering of Takagi–Sugeno fuzzy time‐varying delay systems: Input–output approach