An improved stability criterion for generalized neural networks with additive time-varying delays

Rakkiyappan, R.; Sivasamy, R.; Park, Ju H.; Lee, Tae Hee

doi:10.1016/j.neucom.2015.07.004

Cited by 55 publications

(14 citation statements)

References 40 publications

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“…Therefore, we pointed out particularly, the criteria proposed in this paper there are no restrictions to study the stability,

{scriptH}_{\infty}, {scriptL}_{2} - {scriptL}_{\infty}

, passivity, mixed

{scriptH}_{\infty}

and passivity, and dissipativity performance under the non‐fragile state feedback controller, which are always possible through setting the weighting matrices. Therefore, the analysis technique and system model proposed in this paper is more general than , which differentiates our work more effectively from the previous works.…”

Section: Resultsmentioning

confidence: 95%

“…It should be noted that, the criteria proposed in are restricted to analyzing the dynamical behaviors of GNNs either on stability or

{scriptH}_{\infty}

, or passivity or dissiptivity or stability and dissipativity, individually. Therefore, most available results in only dealt with it separately. It is strongly mentioned that there have been no related works available in the literature to suggest a unified framework analysis in the field of GNNs.…”

Section: Resultsmentioning

confidence: 99%

“…Therefore, recently a unified system model has been taken into consideration is more likable in the study of dynamic analysis (see ), and it is called GNNs. Accordingly, a little attention has been devoted to the study of dynamical analysis of GNNs with time delay ; howbeit, the previous methods in ,

{scriptL}_{2} - {scriptL}_{\infty}

performance is not provided the solutions for GNNs. In , authors have discussed dissipativity and stability analysis of GNNs with Markovian jump parameters and successive time delays using free‐matrix‐based integral inequality approach.…”

Section: Introductionmentioning

confidence: 99%

“…The authors in , discussed stability of fractional‐order delayed neural networks. In , the authors have utilized RCC approach together with some zero equations to derive improved stability results for GNNs with additive time delays in the system model have been investigated. Recently, Manivannan et al.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Non‐Fragile Extended Dissipativity Control Design for Generalized Neural Networks with Interval Time‐Delay Signals

Manivannan

Samidurai

Cao

et al. 2018

Asian Journal of Control

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The problem of non-fragile extended dissipative control design for a class of generalized neural networks (GNNs) with interval time-delay signals is investigated in this paper. By constructing a suitable Lyapunov-Krasovskii functional (LKF) with double and triple integral terms, and estimating their derivative by using the Wirtinger single integral inequality (WSII) and Wirtinger double integral inequality (WDII) technique respectively, and that is mixed with the reciprocally convex combination (RCC) approach. A new delay-dependent non-fragile extended dissipative control design for GNNs are expressed in terms of the linear matrix inequalities (LMIs). Then, the desired non-fragile extended dissipative controller can be obtained by solving the linear matrix inequalities (LMIs). Furthermore, a non-fragile state feedback controller is designed for GNNs such that the closed-loop system is extended dissiptive. Thus, the non-fragile extended dissipative controller can be adopted to deal with the non-fragile  2 − ∞ performance, non-fragile  ∞ performance, non-fragile passive performance, non-fragile mixed  ∞ and passivity performance, and non-fragile dissipative performance for GNNs by selecting the weighting matrices. Finally, simulation studies are demonstrated for showing the feasibility of the proposed method. Among them, one example was supported by the real-life application of the quadruple tank process system.

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“…Therefore, we pointed out particularly, the criteria proposed in this paper there are no restrictions to study the stability,

{scriptH}_{\infty}, {scriptL}_{2} - {scriptL}_{\infty}

, passivity, mixed

{scriptH}_{\infty}

Section: Resultsmentioning

confidence: 95%

“…It should be noted that, the criteria proposed in are restricted to analyzing the dynamical behaviors of GNNs either on stability or

{scriptH}_{\infty}

Section: Resultsmentioning

confidence: 99%

{scriptL}_{2} - {scriptL}_{\infty}

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Non‐Fragile Extended Dissipativity Control Design for Generalized Neural Networks with Interval Time‐Delay Signals

Manivannan

Samidurai

Cao

et al. 2018

Asian Journal of Control

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show abstract

“…For example, in network control systems, signals transmitted from one point to another may experience a few segments of networks, which can possibly induce successive timedelays with different properties due to the variable network transmission conditions [9]. Therefore, the problem of stability criteria for neural networks with successive timevarying delay components have been rarely investigated (see, e.g., [25,28,35,41,46,55]).…”

Section: Introductionmentioning

confidence: 99%

Non-fragile mixed H-infinity and passivity control for neural networks with successive time-varying delay components

Rajavel

Samidurai

Kilbert

et al. 2018

NAMC

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This paper is concerned with the problem of nonfragile mixed H∞ and passivity control for neural networks with successive time-varying delay components. We construct a suitable Lyapunov-Krasovskii function with triple and quadruple integral terms then utilizing Jensen's lemma and Wirtinger-type inequality technique. Some sufficient conditions are presented for the existence of nonfragile mixed H∞ and passivity performance criterions. The expressions for the nonfragile controller can be obtained by solving a set of linear matrix inequality. Finally, two numerical examples are presented to demonstrate the effectiveness of our proposed method.

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New results on stability analysis and extended dissipative conditions for uncertain memristive neural networks with two additive time‐varying delay components and reaction‐diffusion terms

Cao

Xiong

et al. 2020

Intl J Robust & Nonlinear

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This article deals with the problems of exponential stability and extended dissipative analysis for a class of uncertain memristive neural networks (MNNs) with additive time-varying delays and reaction-diffusion terms. On the basis of generalized Lyapunov functional approach, Hardy-Poincarè inequality, Jensen's inequality, as well as some other inequality techniques, it is shown that the issues of exponential stability and extended dissipativity for the uncertain reaction-diffusion MNNs are solvable if a set of linear matrix inequalities (LMIs) proposed are feasible. As a special case, the conditions on exponential stability and extended dissipativity for the uncertain MNNs with additive time-varying delays are also obtained and given in terms of nonlinear matrix inequalities (NMIs). The obtained NMIs can be transformed as general LMIs via using a new quadratic convex combination skill. Moreover, the developed sufficient conditions for the uncertain delayed MNNs with and without reaction-diffusion terms can be easily checked by Matlab LMI control toolbox, and three numerical examples with simulation are provided to show the effectiveness and applicability of the theoretical results.

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An improved stability criterion for generalized neural networks with additive time-varying delays

Cited by 55 publications

References 40 publications

Non‐Fragile Extended Dissipativity Control Design for Generalized Neural Networks with Interval Time‐Delay Signals

Non‐Fragile Extended Dissipativity Control Design for Generalized Neural Networks with Interval Time‐Delay Signals

Non-fragile mixed H-infinity and passivity control for neural networks with successive time-varying delay components

New results on stability analysis and extended dissipative conditions for uncertain memristive neural networks with two additive time‐varying delay components and reaction‐diffusion terms

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