Augmented Lyapunov–Krasovskii functional approaches to robust stability criteria for uncertain Takagi–Sugeno fuzzy systems with time-varying delays

Kwon, Oh‐Min; Park, M. J.; Lee, Sang Moon; Park, Ju H.

doi:10.1016/j.fss.2011.12.014

Cited by 104 publications

(40 citation statements)

References 23 publications

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“…Unlike the complete Lyapunov functional method in [7,10] and the delay partitioning technique in [11,32], in this paper a Lyapunov-Krasovskii functional containing the variable delay-partitioning tuning parameter 0 < δ < 1 is constructed, which means that different delay-partitioning tuning parameter 0 < δ < 1 can obtain different LMI-based stability condition. Our derivation towards Theorem 3.1 also adopts some newly developed integral inequalities (Lemma 2.3) in [23] while the present result is derived by some appropriate integral inequalities in Lemma 2.2.…”

Section: Firstly We Divide the Delay Intervalmentioning

confidence: 99%

See 1 more Smart Citation

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

An¹,

Liu²,

Wen³

2017

J. Nonlinear Sci. Appl.

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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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Section: Firstly We Divide the Delay Intervalmentioning

confidence: 99%

“…For comparisons, we study T-S fuzzy system (2.2) with fuzzy rules investigated in recent publications [1,2,10,12,13,20,21,25,27,32,33].…”

Section: Numerical Examplesmentioning

confidence: 99%

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

An¹,

Liu²,

Wen³

2017

J. Nonlinear Sci. Appl.

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“…Then, the efforts to reduce the conservativeness of the results mainly resumes in constructing new augmented LKF approaches. For example in [75] a triple integral form associated with the so-called Finsler's lemma and some augmented vectors including further information of time-varying delays are exploited. Nevertheless this onward rush led quickly to computational problems due to a huge increase in the number of decision variables.…”

Section: Delaymentioning

confidence: 99%

Fuzzy control turns 50: 10 years later

Guerra

Sala

Tanaka

2015

Fuzzy Sets and Systems

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In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.

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“…Therefore, the stability problem for system with time-delay has received much attention and various analysis methods have thus been proposed. For example, in [15], an augmented Lyapunov-Krasovskii function with a triple integral and some augmented vectors was employed to explore the stability problem of T-S fuzzy systems with time-delay. [16] developed a novel augmented Lyapunov function and a delay-dependent stability condition is proposed.…”

Section: Introductionmentioning

confidence: 99%

“…[16] developed a novel augmented Lyapunov function and a delay-dependent stability condition is proposed. In addition, to further reduce the conservativeness of the results, the various constructions of parameter-dependent Lyapunov-Krasovskii functional methods are developed in many studies [15], [17]- [19]. Nevertheless, few studies explore the stability/stabilization problem for T-S polynomial fuzzy system with time-delay.…”

Section: Introductionmentioning

confidence: 99%

A novel stabilization condition for T-S polynomial fuzzy system with time-delay: A sum-of-squares approach

Tsai

Chen

et al. 2016

2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC)

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, H-K. (2017). A novel stabilization condition for T-S polynomial fuzzy system with time-delay: A sum-of-squares approach. In 2016 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2016 -Conference Proceedings (pp. 1555-1560 General rightsCopyright and moral rights for the publications made accessible in the Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognize and abide by the legal requirements associated with these rights.•Users may download and print one copy of any publication from the Research Portal for the purpose of private study or research.•You may not further distribute the material or use it for any profit-making activity or commercial gain •You may freely distribute the URL identifying the publication in the Research Portal Take down policy If you believe that this document breaches copyright please contact librarypure@kcl.ac.uk providing details, and we will remove access to the work immediately and investigate your claim. Abstract-A novel stabilization problem for T-S polynomial fuzzy system with time-delay is investigated in this paper. Firstly, a polynomial fuzzy controller for T-S polynomial fuzzy system with time-delay is proposed. In addition, based on polynomial Lyapunov-Krasovskii function and the developed polynomial slack variable matrices, a novel stabilization condition for T-S polynomial fuzzy system with time-delay is presented in terms of sum-of-square (SOS) form. Lastly, nonlinear system with timedelay and a well-known T-S fuzzy system with time-delay are illustrated to demonstrate the feasibility and effectiveness of the proposed results.

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Augmented Lyapunov–Krasovskii functional approaches to robust stability criteria for uncertain Takagi–Sugeno fuzzy systems with time-varying delays

Cited by 104 publications

References 23 publications

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

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

Fuzzy control turns 50: 10 years later

A novel stabilization condition for T-S polynomial fuzzy system with time-delay: A sum-of-squares approach

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