Quadratically convex combination approach to stability of T–S fuzzy systems with time-varying delay

Yang, Feisheng; Guan, Shouping; Wang, Dianhui

doi:10.1016/j.jfranklin.2013.01.025

Cited by 49 publications

(24 citation statements)

References 30 publications

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“…For different , the upper bounds of the time-varying delay computed by the proposed method and those in [8,11,20,18,24] are listed in For different , the upper bounds of the time-varying delay computed by the proposed method and those in [5,9,12,24] are listed in …”

Section: Numerical Examplesmentioning

confidence: 99%

“…Recently, in [18], an augmented Lyapunov-Krasovskii functional approach that introduces a triple integral and some augmented vectors was employed to investigate the stability problem of T-S fuzzy systems with time-varying delay. In [20], the improved results was obtained by quadratically convex approach. The results was further improved in [24] by employing the delay-partitioning method and reciprocally convex approach.…”

Section: Introductionmentioning

confidence: 99%

“…First, in [8,11,20,18], Jensen's inequality, free-weighting matrix and quadratically convex combination approach are used to derive the stability condition. However, reciprocally convex approach [25], which can play an important role in reducing conservatism of the stability condition, is not used in [8,11,20,18]. Second, though the reciprocal convex approach, delay-partitioning and integral inequalities method are combined to obtain some less conservative results in [24], it still needs some improvements since it only used the improved inequality in constant delay, not employed in time-varying delay.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust Delay-dependent Stability Criteria for Takagi-Sugeno Fuzzy Systems with Time-varying Delay

Liu

Lee

Kwon³

2015

The Transactions of The Korean Institute of Electrical Engineer

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-This paper presents the robust stability condition of uncertain Takagi-Sugeno(T-S) fuzzy systems with time-varying delay. New augmented Lyapunov-Krasovskii function is constructed to ensure that the system with time-varying delay is globally asymptotically stable. Also, less conservative delay-dependent stability criteria are obtained by employing some integral inequality, reciprocally convex approach and new delay-partitioning method. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

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Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Delay-dependent Stability Criteria for Takagi-Sugeno Fuzzy Systems with Time-varying Delay

Liu

Lee

Kwon³

2015

The Transactions of The Korean Institute of Electrical Engineer

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“…The delay upper bound results for a given 1 (delay lower bound) for slow and fast varying delay compared to existing results are presented in Table I and II respectively. Example 2: Consider a time-delayed fuzzy system in [38], Plant Rule 1: ] .…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…In recent years, the problems of stability and stabilization of the T-S fuzzy systems with time delay have attracted rapidly growing interest's [24], [39], [30], [29], [41]. More specifically, related to the problem of checking stability for T-S fuzzy systems with interval timevarying delays one can find recent works as [37], [38] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Improved delay-range-dependent stability analysis of a T-S Fuzzy system with time varying delay

Dey

Balas

Lin

et al. 2013

2013 IEEE 14th International Symposium on Computational Intelligence and Informatics (CINTI)

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This paper presents a new & improved stability analysis for Takagi-Sugeno (T-S) Fuzzy system subjected to interval time-varying delay. The stability analysis provides a sufficient stability condition in an Linear Matrix Inequality (LMI) frame work that can estimate less conservative delay upper bound for a given lower bound of delay. The analysis is carried out by proposing new and modified Lyapunov-Krasovskii (L-K) functional along with the judicious use of Jensen's integral for eliminating the integral terms arising out from the time derivative of L-K functional, these modifications in turn leads to convex combination of the LMIs. Few numerical examples are included to illustrate the effectiveness of the obtained stability condition compared to some recently published stability conditions for different delay nature while delay is varying in intervals.

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Further Studies on Stability and Stabilization of T‐S Fuzzy Systems With Time‐Varying Delays via Fuzzy Lyapunov‐Krasovskii Functional Method

Tan

Dian

Zhao

2017

Asian Journal of Control

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This paper discusses the issue of stability analysis and stabilization of Takagi-Sugeno (T-S) fuzzy systems with time-varying delays. By constructing an appropriate augmented fuzzy Lyapunov-Krasovskii functional (LKF) including non-quadratic Lyapunov matrices and triple and quadruple integral term,less conservative and newer stability conditions are introduced. In order to obtain stability conditions in the form of linear matrix inequalities (LMIs), some tighter bounding inequalities are employed to estimate the derivative of LKF. Several examples are provided to illustrate the effectiveness of the suggested approaches.

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Quadratically convex combination approach to stability of T–S fuzzy systems with time-varying delay

Cited by 49 publications

References 30 publications

Robust Delay-dependent Stability Criteria for Takagi-Sugeno Fuzzy Systems with Time-varying Delay

Robust Delay-dependent Stability Criteria for Takagi-Sugeno Fuzzy Systems with Time-varying Delay

Improved delay-range-dependent stability analysis of a T-S Fuzzy system with time varying delay

Further Studies on Stability and Stabilization of T‐S Fuzzy Systems With Time‐Varying Delays via Fuzzy Lyapunov‐Krasovskii Functional Method

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