An integral inequality in the stability problem of time-delay systems

Gu, Keqin

doi:10.1109/cdc.2000.914233

Cited by 1,007 publications

(448 citation statements)

References 17 publications

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“…Lemma 3: [7] For any positive definite matrix M > 0, scalar γ > 0, vector function ω : [0, γ] → R n such that the integrations concerned are well defined, the following inequality holds:…”

Section: Main Results and Proofsmentioning

confidence: 99%

Design of exponential state estimators for neural networks with mixed time delays

2007

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In this paper, the state estimation problem is dealt with for a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. The activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. We aim at designing a state estimator to estimate the neuron states, through available output measurements, such that the dynamics of the estimation error is globally exponentially stable in the presence of mixed time delays. By using the Laypunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.

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Section: Main Results and Proofsmentioning

confidence: 99%

Design of exponential state estimators for neural networks with mixed time delays

2007

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“…According to Theorem 8.3, p303, [9], there exists a unique continuous solution denoted by x(t; ξ) or simply x(t) to equation (1). It is known (see, e.g., [9]) that {x t , r(t)} t≥0 is a…”

Section: Problem Statementmentioning

confidence: 99%

“…In this paper, we are to establish new delay-dependent sufficient conditions for robust exponential stability of uncertain stochastic delay system with Markovian switching (1). For simplicity only, we take single delay h in our model.…”

Section: Problem Statementmentioning

confidence: 99%

Delay-dependent robust stability of stochastic delay systems with Markovian switching

Huang

Mao

Deng

2009

J. Control Theory Appl.

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This version is available at https://strathprints.strath.ac.uk/16872/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Abstract: In recent years, stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities (LMIs), which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.

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“…Therefore, it is of practical importance to study the stochastic effects on the stability property of delayed neural networks, see for example [3][4][5][6]11,16,18,19,23,27,29]. Also, there are systems which are with some nonzero delays, but they are unstable without delay [7,8,30]. Therefore, it is important to perform the stability analysis systems with nonzero delays [22] and the non-zero delay can be placed into a given interval.…”

Section: Introductionmentioning

confidence: 99%

Delay-dependent exponential stability results for uncertain stochastic Hopfield neural networks with interval time-varying delays

2012

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This paper is concerned with stability analysis problem for uncertain stochastic neural networks with interval time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Both the cases of the time-varying delays which may be differentiable and may not be differentiable are considered in this paper. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay/interval-dependent stability criteria are obtained in terms of linear matrix inequalities. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), by introducing some free-weighting matrices. Finally, three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions. Mathematics Subject Classification (2010) 34K20 · 34K50 · 92B20

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An integral inequality in the stability problem of time-delay systems

Cited by 1,007 publications

References 17 publications

Design of exponential state estimators for neural networks with mixed time delays

Design of exponential state estimators for neural networks with mixed time delays

Delay-dependent robust stability of stochastic delay systems with Markovian switching

Delay-dependent exponential stability results for uncertain stochastic Hopfield neural networks with interval time-varying delays

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