Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays

Zhu, Quanxin; Xi, Fubao; Li, Xiaodi

doi:10.1007/s10957-012-9997-5

Cited by 32 publications

(22 citation statements)

References 27 publications

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“…Combining with the results obtained in , another extension can be presented for nonlinear stochastic composite systems with singular perturbations. The main criterion can be considered in the stochastically nonlinear jump systems with time delays . The results are sufficient conditions, for which conservatism is inevitable.…”

Section: Conclusion and Final Remarksmentioning

confidence: 99%

Stability Analysis of Stochastic Interconnected Systems by Vector Lyapunov Function Method

Shi¹,

Zhang²,

Xu³

et al. 2015

Asian Journal of Control

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In this paper, the interconnecting structure between a certain system and its lower order subsystems within the infinitedimension stochastic interconnected systems is analyzed. Assuming that the excitations are parametric white noises, the exponential string stability for a few classes of nonlinear stochastic interconnected systems is discussed. By using the vector Lyapunov function method, the sufficient conditions of exponential string stability are derived, expanding the scope of the parameters for systems stability. Moreover, some cases of exponential string stability for vehicle-following systems in automated highway systems are specified. Finally, an example is shown to illustrate the proposed method.

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Section: Conclusion and Final Remarksmentioning

confidence: 99%

Stability Analysis of Stochastic Interconnected Systems by Vector Lyapunov Function Method

Shi¹,

Zhang²,

Xu³

et al. 2015

Asian Journal of Control

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“…It is inspiring that many important results have been reported in the literature. For example, Zhu et al [10] investigated the problem of robust exponential stability for a class of stochastically nonlinear jump systems with mixed time delays. Zhu [11] investigated the th moment exponential stability for a class of impulsive stochastic functional differential equations with Markovian switching (SFDEwMs).…”

Section: Introductionmentioning

confidence: 99%

Stability of a Class of Hybrid Neutral Stochastic Differential Equations with Unbounded Delay

Song

2017

Discrete Dynamics in Nature and Society

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This paper studies the stability of hybrid neutral stochastic differential equations with unbounded delay. Some novel exponential stability criteria and boundedness conditions are established based on the generalized Itô formula and Lyapunov functions. The factor − ( ) is used to overcome the difficulties caused by the unbounded delay ( ) effectively. In particular, our results generalize and improve some previous stability results from bounded delay to unbounded delay conditions. Finally, an example is presented to demonstrate the effectiveness of the proposed results.

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“…On the other hand, time delays, which commonly appear in practical systems, are often the cause of instability. Hence the stability of stochastic delay systems is always the hot area in many researches [10,17,18,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

pth Moment exponential stability of stochastic delayed hybrid systems with Lévy noise

Zhou

Yang

et al. 2015

Applied Mathematical Modelling

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In this paper, the problem of pth moment exponential stability analysis is considered for stochastic delayed hybrid systems with Lévy noise. By the technique of stochastic analysis as well as M-matrix theories, we propose some sufficient conditions to guarantee the exponential stability of the system. The criterion of mean square exponential stability for delayed neural networks with Lévy noise is derived as well. A numerical example is provided to show the usefulness of the proposed exponential stability criterion.

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Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays

Cited by 32 publications

References 27 publications

Stability Analysis of Stochastic Interconnected Systems by Vector Lyapunov Function Method

Stability Analysis of Stochastic Interconnected Systems by Vector Lyapunov Function Method

Stability of a Class of Hybrid Neutral Stochastic Differential Equations with Unbounded Delay

pth Moment exponential stability of stochastic delayed hybrid systems with Lévy noise

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