Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays

He, Yong; Wu, Min; She, Jinhua; Liu, Shuai

doi:10.1016/s0167-6911(03)00207-x

Cited by 642 publications

(472 citation statements)

References 17 publications

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“…Remark 3.1 In the proof of this theorem, the functional V is general for considering much more information about the state vector. In particular, 5 V is very important to improve the delay-dependent stability condition. If one attempt to delete   x t   from 1 G or 2 G , the maximum of time-delay may less than those of original 5 V .…”

Section: X T P Ax T Bx T H Cx T Hmentioning

confidence: 99%

“…In the past two decades, a great deal of attention have been drawn to the delay-dependent stability problem of neutral dynamical systems (see, e.g., [1]- [31]). Various important methods have been introduced, such as model transformation approach [4], delay partitioning technique [11], discretized Lyapunov functional method [12], free-weighting matrix approach [5], and descriptor system approach [17]. Among those techniques, the Jensen's like inequality has played an important role to obtain delay-dependent stability conditions [21].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Novel Stability Criterion for Neutral Systems with Mixed Time-Delay

Xiong¹,

Li²,

Wu³

et al. 2016

Proceedings of the 2016 International Conference on Applied Mathematics, Simulation and Modelling

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Abstract-The aim of this paper is to improve stability condition for neutral systems with mixed time-delay. By introducing a novel integral inequality based on the optimization theory, and constructing the novel Lyapunov functionals, an improved delaydependent stability criterion is established. It is shown that the integral inequality obtained in this paper can be utilized to get less conservative delay-dependent stability condition for neutral systems. A numerical example is provided to demonstrate the theoretical result.

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Section: X T P Ax T Bx T H Cx T Hmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Novel Stability Criterion for Neutral Systems with Mixed Time-Delay

Xiong¹,

Li²,

Wu³

et al. 2016

Proceedings of the 2016 International Conference on Applied Mathematics, Simulation and Modelling

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show abstract

“…Example 1: In this example, we consider a somewhat arbitrarily chosen example to illustrate the delay-dependent stability condition associated with Theorem4. We use the example chosen by [4], [6], and [5] among many others. This can be done automatically in Matlab using the function cpoly2rpoly contained in the software package available online at [8].…”

Section: Verifying the Datko Conditionsmentioning

confidence: 99%

SOS Methods for Stability Analysis of Neutral Differential Systems

Peet¹,

Bonnet²,

Özbay

2009

Topics in Time Delay Systems

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Summary. This paper gives a description of how "sum-of-squares" (SOS) techniques can be used to check frequency-domain conditions for the stability of neutral differential systems. For delay-dependent stability, we adapt an approach of Zhang et al. [10] and show how the associated conditions can be expressed as the infeasibility of certain semialgebraic sets. For delay-independent stability, we propose an alternative method of reducing the problem to infeasibility of certain semialgebraic sets. Then, using Positivstellensatz results from semi-algebraic geometry, we convert these infeasibility conditions to feasibility problems using sum-of-squares variables. By bounding the degree of the variables and using the Matlab toolbox SOSTOOLS [7], these conditions can be checked using semidefinite programming

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“…Various interesting methods have been introduced to obtain delay-dependent stability conditions for neutral delay systems, such as model transformation approach [8], delay partitioning technique [2], discretized Lyapunov functional method [11], free-weighting matrix approach [9,12], and integral inequality method [1]. With the help of these approaches, improved delay-dependent stability conditions have been presented gradually, such as [3,11,15] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Improved conditions for neutral delay systems with novel inequalities

Xiong¹,

Cheng²,

Liu³

et al. 2017

J. Nonlinear Sci. Appl.

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This paper studies the stability problem of a class of neutral delay systems. It firstly establishes two novel integral inequalities, which are better than the same type inequalities found in the literature. Then it derives, by using the new inequalities and the Lyapunov functional method, some sufficient delay-dependent conditions for asymptotic stability of the neutral delay systems. Three numerical examples are provided to illustrate the advantage and effectiveness of the obtained results.

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Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays

Cited by 642 publications

References 17 publications

Novel Stability Criterion for Neutral Systems with Mixed Time-Delay

Novel Stability Criterion for Neutral Systems with Mixed Time-Delay

SOS Methods for Stability Analysis of Neutral Differential Systems

Improved conditions for neutral delay systems with novel inequalities

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