Multiple integral inequalities and stability analysis of time delay systems

Gyurkovics, Éva; Takács, Tibor

doi:10.1016/j.sysconle.2016.07.002

Cited by 42 publications

(21 citation statements)

References 20 publications

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“…The following neural networks (27) with randomly occurring uncertain parameters is the extension of NNs (2). Now the remodified neural networks of (27) as follows…”

Section: Randomly Occurring Uncertain Discrete Time Neural Networkmentioning

confidence: 99%

“…The authors in [25] proposed the concept of novel summation inequalities with time-varying delays to check the stability of neural networks. The results on Wirtinger based inequality has been proved by authors [26,27]. Liu in [28,29] investigated the impact of stability in exponential sense for discrete time BAM neural networks with some novel criterions and in [30] authors proposed discrete-time BAM neural networks in the sense of exponential.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A delay‐dependent asymptotic stability criteria for uncertain BAM neural networks with leakage and discrete time‐varying delays: A novel summation inequality

Sowmiya¹,

Raja

Cao

et al. 2019

Asian Journal of Control

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This proposed research work aims to investigate the problem of uncertain BAM neural networks with leakage and discrete time‐varying delays in the sense of asymptotic stable by applying convex combination approach, discrete‐time Wirtinger inequality. It is pointed out that a novel summation inequality is entrenched based on discrete type Wirtinger based inequality. By the aid of novel inequality, reciprocally convex combination technique, time‐varying delays are examined to certify the stability of neural networks. Here, the uncertainties are considered as a randomly occurring parameter uncertainties and it conforms certain mutually uncorrelated Bernoulli‐distributed white noise sequences. The important feature of the results reported here is that the probability of occurrence of the parameter uncertainties are known a priori. To demonstrate the theoretical results of this research paper, numerical examples are given to expo the validity and efficiency of our results with the help of LMI Control toolbox in matlab.

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“…The following neural networks (27) with randomly occurring uncertain parameters is the extension of NNs (2). Now the remodified neural networks of (27) as follows…”

Section: Randomly Occurring Uncertain Discrete Time Neural Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A delay‐dependent asymptotic stability criteria for uncertain BAM neural networks with leakage and discrete time‐varying delays: A novel summation inequality

Sowmiya¹,

Raja

Cao

et al. 2019

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…To the best of our knowledge, Gouaisbaut & Ariba (2011) is the only published paper to be able to handle range stability analysis for systems having a distributed delay with polynomials kernels. Meanwhile, Example 2 cannot be analyzed by the range stability results in Gyurkovics & Takács (2016); ; Gouaisbaut et al (2013).…”

Section: Delay Range Stability Analysismentioning

confidence: 99%

Dissipative delay range analysis of coupled differential–difference delay systems with distributed delays

Feng

Nguang

2018

Systems & Control Letters

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This paper proposes methods to handle the problem of delay range stability analysis for a linear coupled differential-difference system (CDDS) with distributed delays subject to dissipative constraints. The model of linear CDDS contains many models of linear delay systems as special cases. A novel Liapunov-Krasovskii functional with non-constant matrix parameters, which are related to the delay value polynomially, is applied to derive stability conditions. By constructing this new functional, sufficient conditions in terms of robust linear matrix inequalities (LMIs) can be derived, which guarantee range stability of a linear CDDS subject to dissipative constraints. To solve the resulting robust LMIs numerically, we apply the technique of sum of squares programming together with matrix relaxations without introducing any potential conservatism to the original robust LMIs. Furthermore, the proposed methods can be extended to solve delay margin estimation problems for a linear CDDS subject to prescribed dissipative constraints. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methodologies.

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“…The stability analysis and stabilization of time-delay systems have been tackled over because time delays occur in many practical systems, such as those in the fields of aeronautics, chemistry, and mechanics [1]. There are many valuable results regarding the stability analysis and stabilization of time delay systems [2][3][4]. Generally speaking, delaydependent stability conditions are less conservative than delay-independent ones, especially when the time delays are relatively small.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis for uncertain neutral-type stochastic nonlinear systems with mixed time-varying delays

2019

J Inequal Appl

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This study investigates the robust stability problem in the presence of uncertain parameters for a class of stochastic neutral-type systems with mixed time-varying delays, where external disturbance and nonlinearity are considered together. The nonlinear function is assumed to satisfy the one-sided Lipschitz condition and the quadratic inner-boundedness condition. By constructing a modified Lyapunov-Krasovskii functional and using the free-weighting matrix technique, some new delay-dependent criteria for the stability of the problem are presented. In particular, the derivatives of the time-varying delays are no longer limited to being less than one. Finally, numerical examples are given to illustrate the effectiveness of the derived results.

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Multiple integral inequalities and stability analysis of time delay systems

Abstract: This paper is devoted to stability analysis of continuous-time delay systems based on a set of LyapunovKrasovskii functionals. New multiple integral inequalities are derived that involve the famous Jensen's and

Cited by 42 publications

References 20 publications

A delay‐dependent asymptotic stability criteria for uncertain BAM neural networks with leakage and discrete time‐varying delays: A novel summation inequality

A delay‐dependent asymptotic stability criteria for uncertain BAM neural networks with leakage and discrete time‐varying delays: A novel summation inequality

Dissipative delay range analysis of coupled differential–difference delay systems with distributed delays

Stability analysis for uncertain neutral-type stochastic nonlinear systems with mixed time-varying delays

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