Delay-partitioning approach for systems with interval time-varying delay and nonlinear perturbations

Hui, Junjun; Kong, Xiangyu; Zhang, Hexin; Zhou, Xin

doi:10.1016/j.cam.2014.11.060

Cited by 41 publications

(14 citation statements)

References 30 publications

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“…By utilizing the schur lemma, (55) < 0 can be equivalent to (18). Hence, E{LV (x t , i, t)} 0, according to Definition 1 in [17], the neutral-type neural networks with Markovian jumping parameters (2) is proved to be robustly stochastically stable in the mean square.…”

Section: Resultsmentioning

confidence: 92%

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Delay-partitioning approach design for stochastic stability analysis of uncertain neutral-type neural networks with Markovian jumping parameters

et al. 2016

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Section: Resultsmentioning

confidence: 92%

“…After that the delay-partition idea was firstly proposed in [17], many researchers have focused on designing delay-partition technologies [18][19][20][21][22][23]. For example, the reference [23] considered a delay partitioning approach to delay-dependent stability analysis for neutral type neural networks.…”

Section: Introductionmentioning

confidence: 99%

Delay-partitioning approach design for stochastic stability analysis of uncertain neutral-type neural networks with Markovian jumping parameters

et al. 2016

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“…Then previous developed research works using the equivalent partition method Hui et al. (2015), Wang and Shen (2012), Zhao et al. (2009) can be considered as a special case of this proposed approach.…”

Section: Resultsmentioning

confidence: 99%

Improved results on nonlinear perturbed T–S fuzzy systems with interval time-varying delays using a geometric sequence division method

Chen

2016

SpringerPlus

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This paper presents improved stability results by introducing a new delay partitioning method based on the theory of geometric progression to deal with T–S fuzzy systems in the appearance of interval time-varying delays and nonlinear perturbations. A common ratio is applied to split the delay interval into multiple unequal subintervals. A modified Lyapunov–Krasovskii functional (LKF) is constructed with triple-integral terms and augmented factors including the length of every subintervals. In addition, the recently developed free-matrix-based integral inequality is employed to combine with the extended reciprocal convex combination and free weight matrices techniques for avoiding the overabundance of the enlargement when deducing the derivative of the LKF. Eventually, this developed research work can efficiently obtain the maximum upper bound of the time-varying delay with much less conservatism. Numerical results are conducted to illustrate the remarkable improvements of this proposed method.

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“…A number of recent endeavours for improving the stability criteria of interval time-varying delay systems have been devoted to modifying the LKF, and other attempts have focused on reducing the conservatism of the used techniques for estimating the LKF's derivative. The methods of the first group include delay partitioning and delay decomposition schemes, 8,9,12,[15][16][17] using multiple-integral terms, 9,10,12,[18][19][20] and using slack variables or zero equations. 8,15 A number of those schemes can result in the excessive number of decision variables that can imply computational difficulties.…”

mentioning

confidence: 99%

“…On the other hand, methods like using convex combination technique, 8,9,19 reciprocally convex combination approach, 12,17,18,[21][22][23] and less conservative integral inequalities 17,20 can effectively reduce the conservatism of the derived stability criteria, while minimally adding to the number of decision variables.…”

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confidence: 99%

New delay range–dependent stability criteria for interval time‐varying delay systems via Wirtinger‐based inequalities

Mohajerpoor

Shanmugam

Asayesh

et al. 2017

Intl J Robust & Nonlinear

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Summary Stability conditions for time‐delay systems using the Lyapunov‐based methodologies are generically expressed in terms of linear matrix inequalities. However, due to assuming restrictive conditions in deriving the linear matrix inequalities, the established stability conditions can be strictly conservative. This paper attempts to relax this problem for linear systems with interval time‐varying delays. A double‐integral inequality is derived inspired by Wirtinger‐based single‐integral inequality. Using the advanced integral inequalities, the reciprocally convex combination techniques and necessary slack variables, together with extracting a condition for the positive definiteness of the Lyapunov functional, novel stability criteria, have been established for the system. The effectiveness of the criteria is evaluated via 2 numerical examples. The results indicate that more complex stability criteria not only improve the stability region but also bring computational expenses.

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Delay-partitioning approach for systems with interval time-varying delay and nonlinear perturbations

Cited by 41 publications

References 30 publications

Delay-partitioning approach design for stochastic stability analysis of uncertain neutral-type neural networks with Markovian jumping parameters

Delay-partitioning approach design for stochastic stability analysis of uncertain neutral-type neural networks with Markovian jumping parameters

Improved results on nonlinear perturbed T–S fuzzy systems with interval time-varying delays using a geometric sequence division method

New delay range–dependent stability criteria for interval time‐varying delay systems via Wirtinger‐based inequalities

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