Exponential estimates for neutral time-delay systems: an LMI approach

Kharitonov, Vladimir L.; Mondié, Sabine; Collado, Joaquı́n

doi:10.1109/tac.2005.846595

Cited by 71 publications

(9 citation statements)

References 10 publications

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“…According to the results of Vladimir et al [25], for ε ∈ (0, 1), there is the freedom to choose r smaller at the cost of slower decay rate, when ε is close to 1, or if ε is close to 0, a larger r and a faster decay rate is obtained.…”

Section: Remarkmentioning

confidence: 99%

A semi-free weighting matrices approach for neutral-type delayed neural networks

Mai

Liao

2009

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this paper, a new approach is proposed for stability issues of neutral-type neural networks (DNNs) with constant delay. First, the semi-free weighting matrices are proposed and used instead of the known free weighting matrices to express the relationship between the terms in the Leibniz-Newton formula to simplify the system synthesis and to obtain less computation demand. Second, global exponential stability conditions which are less conservative and restrictive than the known results are derived. At the same time, based on the above approach, fewer variable matrices are introduced in the construction of the Lyapunov functional and augmented Lyapunov functional. Two examples are given to show their effectiveness and advantages over others.

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Section: Remarkmentioning

confidence: 99%

A semi-free weighting matrices approach for neutral-type delayed neural networks

Mai

Liao

2009

Journal of Computational and Applied Mathematics

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“…[24] For a given matrixB, if there exist a positive definite matrix Γ and a scalar η ∈ (0, 1) such that…”

Section: Complex Dynamical Network Model and Preliminariesmentioning

confidence: 99%

Synchronization and exponential estimates of complex networks with mixed time-varying coupling delays

Yang

Cai

2009

Int. J. Autom. Comput.

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Exponential estimates and sufficient conditions for the exponential synchronization of complex dynamical networks with bounded time-varying delays are given in terms of linear matrix inequalities (LMIs). A generalized complex networks model involving both neutral delays and retarded ones is presented. The exponential synchronization problem of the complex networks is converted equivalently into the exponential stability problem of a group of uncorrelated delay functional differential equations with mixed timevarying delays. By utilizing the free weighting matrix technique, a less conservative delay-dependent synchronization criterion is derived. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

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“…The traditional approaches to problems of stability of time-varying differential equations of neutral type are based on the Lyapunov's method and its variants, see e.g. [4]- [10], [12]- [16], [18], [19]. Most existing results in the literature are given in terms of matrix inequalities and not straightforward to use.…”

Section: Introductionmentioning

confidence: 99%

“…To illustrate the advantage of the results of this paper, we present a numerical example for which the stability criteria given in [1], [7], [16], [18] cannot be applied.…”

mentioning

confidence: 99%

On exponential stability of linear non-autonomous functional differential equations of neutral type

Ngoc

2016

International Journal of Control

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General linear non-autonomous functional differential equations of neutral type are considered. A novel approach to exponential stability of neutral functional differential equations is presented. Consequently, explicit criteria are derived for exponential stability of linear non-autonomous functional differential equations of neutral type. A brief discussion to the obtained results and illustrative examples are given. 1991 Mathematics Subject Classification. 34K20.

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Exponential estimates for neutral time-delay systems: an LMI approach

Cited by 71 publications

References 10 publications

A semi-free weighting matrices approach for neutral-type delayed neural networks

A semi-free weighting matrices approach for neutral-type delayed neural networks

Synchronization and exponential estimates of complex networks with mixed time-varying coupling delays

On exponential stability of linear non-autonomous functional differential equations of neutral type

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