The Razumikhin approach on general decay stability for neutral stochastic functional differential equations

Pavlović, Gorica; Janković, Svetlana

doi:10.1016/j.jfranklin.2013.05.025

Cited by 29 publications

(24 citation statements)

References 23 publications

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“…Remark 3: In Theorem 2, based on an ordinary technique of the functional differential equations, the delaydependent exponential stability criteria for the NSMSs with time-varying delay (1) are captured, and the method to compute the time-varying delay's least upper bound τ * is given in (12). This technique can be utilized to solve the problem in this section in that it is benefited from inequality (4) and the Lyapunov function (15).…”

Section: B Delay-dependent Exponential Stability For the Nsmss With mentioning

confidence: 99%

“…While effective, the obtained results in [4]- [7] are only applicable to the constant delay systems. Although, in [3] and [10]- [12], the Razumikhin-type theorem has been extended to investigate the exponential stability in pth(p > 1)-moment for the neutral stochastic systems, the obtained sufficient condition is difficult to be verified. Inspired by the ideas in [4]- [7], some authors have focused on the stability analysis for neutral stochastic systems with time-varying delay in [13] and [14], but one important restrictive condition that the derivative value of timevarying delay is less than one must be imposed.…”

Section: Introductionmentioning

confidence: 99%

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Exponential Stability for Neutral Stochastic Markov Systems With Time-Varying Delay and Its Applications

Chen

Shi

Lim

et al. 2016

IEEE Trans. Cybern.

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In this paper, the exponential stability in p th( p > 1 )-moment for neutral stochastic Markov systems with time-varying delay is studied. The derived stability conditions comprise two forms: 1) the delay-independent stability criteria which are obtained by establishing an integral inequality and 2) the delay-dependent stability criteria which are captured by using the theory of the functional differential equations. As its applications, the obtained stability results are used to investigate the exponential stability in p th( p > 1 )-moment for the neutral stochastic neural networks with time-varying delay and Markov switching, and the globally exponential adaptive synchronization for the neutral stochastic complex dynamical systems with time-varying delay and Markov switching, respectively. On the delay-independent criteria, sufficient conditions are given in terms of M -matrix and thus are easy to check. The delay-dependent criteria are presented in the forms of the algebraic inequalities, and the least upper bound of the time-varying delay is also provided. The primary advantages of these obtained results over some recent and similar works are that the differentiability or continuity of the delay function is not required, and that the difficulty stemming from the presence of the neutral item and the Markov switching is overcome. Three numerical examples are provided to examine the effectiveness and potential of the theoretic results obtained.

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Section: B Delay-dependent Exponential Stability For the Nsmss With mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exponential Stability for Neutral Stochastic Markov Systems With Time-Varying Delay and Its Applications

Chen

Shi

Lim

et al. 2016

IEEE Trans. Cybern.

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“…When such systems are subject to environmental disturbances, they can be characterized by neutral stochastic differential delay equations . The stability analysis and some control problems for neutral stochastic delay systems have been extensively investigated because stochastic model can be applied into many branches of science and engineering fields . For example, in , by utilizing Razumikhin‐type theorem, Pavlovi ć and Jankovi ć have considered the general decay stability for neutral stochastic functional differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…The stability analysis and some control problems for neutral stochastic delay systems have been extensively investigated because stochastic model can be applied into many branches of science and engineering fields . For example, in , by utilizing Razumikhin‐type theorem, Pavlovi ć and Jankovi ć have considered the general decay stability for neutral stochastic functional differential equations. In , Luo et al have given some new criteria on the exponential stability for neutral stochastic differential delay equations by establishing the Lyapunov theorem.…”

Section: Introductionmentioning

confidence: 99%

Stability of neutral stochastic switched time delay systems: An average dwell time approach

Chen

Shi

Lim

2016

Int. J. Robust. Nonlinear Control

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This paper considers a class of stochastic systems referred to as stochastic switched systems of neutral type with time-varying delay, which combines switched systems with neutral stochastic systems. The systems consist of subsystems of two forms: (i) only stable subsystems and (ii) both stable subsystems and unstable subsystems. By establishing an integral inequality, the exponential stability in pth .p > 1/-moment for such systems with only stable subsystems is first considered. Then, by using an average dwell time approach, the exponential stability in pth .p > 1/-moment for the second form is addressed. An important finding of this study is that when the average dwell time is chosen to be sufficiently large and the total activation time of unstable subsystems is relatively small compared with that of stable subsystems, the exponential stability in pth .p > 1/-moment for such systems can be guaranteed. Two major advantages of these new results are that the differentiability or continuity of the delay function is not required compared with the existing results in the literature, and the proposed approaches can be used to consider the case when the neutral item and the stochastic perturbation are simultaneously presented. An example is provided to verify the effectiveness and potential of the theoretic results obtained. STOCHASTIC SWITCHED TIME DELAY SYSTEMS 513 dealing with time-varying delay while using the methods proposed in [2][3][4][5][6][7][8][9][10][11] Chen et al. in [12,13] have derived an integral inequality to deal with the exponential stability for neutral stochastic systems with time-varying delay and Markovian switching.A switched system is a hybrid dynamical system that is composed of a finite number of subsystems and a logical rule that orchestrates switching between the subsystems [14]. Because switched systems can be employed to describe many practical systems [15][16][17][18][19][20][21][22][23][24], stability analysis and switching control design for such systems have been extensively studied, for example, [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] and the references therein. In [26], Zhai et al. have investigated the stability analysis of switched systems with continuous-time and discrete-time subsystems by using the Lie algebra approach. In [27], by using a Riccati-type Lyapunov functional, the stability analysis for a class of linear switching systems with time delay was conducted. However, in [26,27], the authors only discussed switched systems with stable subsystems, and the unstable subsystems were not dealt with. In fact, in hybrid switched systems, unstable subsystems are ubiquitous [25]. In [28], an average dwell time approach is first introduced to discuss the stability analysis for switched systems with both stable subsystems and unstable subsystems. As pointed out in [14], the average dwell time switching is a class of restricted switching signals which means that the average time between consecutive switching is not less than a constant [25][26...

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“…The stability of neutral stochastic system with delays has been studied in many papers (see for example [6], [13], [17], [19] and the references therein). However, the problem W. Aggoune of stabilizing neutral stochastic systems with delay in a nonlinear context remains an open problem.…”

Section: Introductionmentioning

confidence: 99%

On stabilization of neutral stochastic differential delay systems

Aggoune

Gennaro

2015

2015 American Control Conference (ACC)

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In this paper the stabilization problem for a class of neutral stochastic systems with delay is investigated. The state equations are described by an Itô differential equation driven by a Wiener noise. The input generically enters both in the deterministic dynamics and in those affected by noise. The considered systems are nonlinear and nonaffine in the control. By using the Razumikhin-type approach, general conditions are developed for stabilizing the closed-loop system. A stabilizing state feedback control is also derived.

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The Razumikhin approach on general decay stability for neutral stochastic functional differential equations

Cited by 29 publications

References 23 publications

Exponential Stability for Neutral Stochastic Markov Systems With Time-Varying Delay and Its Applications

Exponential Stability for Neutral Stochastic Markov Systems With Time-Varying Delay and Its Applications

Stability of neutral stochastic switched time delay systems: An average dwell time approach

On stabilization of neutral stochastic differential delay systems

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