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1.
This paper investigates the pth moment exponential stability of impulsive stochastic functional differential equations. Some sufficient conditions are obtained to ensure the pth moment exponential stability of the equilibrium solution by the Razumikhin method and Lyapunov functions. Based on these results, we further discuss the pth moment exponential stability of generalized impulsive delay stochastic differential equations and stochastic Hopfield neural networks with multiple time-varying delays from the impulsive control point of view. The results derived in this paper improve and generalize some recent works reported in the literature. Moreover, we see that impulses do contribute to the stability of stochastic functional differential equations. Finally, two numerical examples are provided to demonstrate the efficiency of the results obtained. 相似文献
2.
In this paper, the pth moment exponential stability for a class of impulsive stochastic functional differential equations with Markovian switching is investigated. Based on the Lyapunov function, Dynkin formula and Razumikhin technique with stochastic version as well as stochastic analysis theory, many new sufficient conditions are derived to ensure the pth moment exponential stability of the trivial solution. The obtained results show that stochastic functional differential equations with/without Markovian switching may be pth moment exponentially stabilized by impulses. Moreover, our results generalize and improve some results obtained in the literature. Finally, a numerical example and its simulations are given to illustrate the theoretical results. 相似文献
3.
By using the Razumikhin-type technique, for stochastic discrete-time delay systems, this paper establishes the discrete Razumikhin-type theorems on the pth moment stability, the global pth moment stability and the pth moment exponential stability, respectively. The almost sure exponential stability is also investigated by using the pth moment exponential stability and the Borel–Cantelli lemma. As the applications of t he established theorems, stability of a special class of stochastic discrete-time delay systems, synchronization of the stochastic discrete-time delay dynamical networks and stabilization of a stochastic discrete-time linear delay time invariant system are examined. 相似文献
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This paper investigates pth moment boundedness of neutral stochastic functional differential equations with Markovian switching (NSFDEsMS) based on Razumikhin technique and comparison principle. And pth moment stability is examined as a special case. Since the stochastic disturbances and neutral delays are incorporated, the considered system becomes more complex. Besides, the coefficients of the estimated upper bound for the diffusion operation associated with the underlying NSFDEsMS also may be chosen to be sign-changing functions instead of constant functions or negative definite functions, as a result, our results can work in general non-autonomous neutral stochastic systems. Finally, two examples are provided to show the effects of the proposed methods. 相似文献
5.
在现有文献的基础上，对一类马尔可夫调制的随机微分方程进行了研究，得到了其平凡解2阶均值指数稳定性和几乎必然指数稳定性的充分条件。对现有成果进行了改进。 相似文献
6.
This paper gives some Razumikhin-type theorems on pth moment boundedness of stochastic functional differential equations with Markovian switching (SFDEwMS) by using Razumikhin technique and comparison principle. Some improved conditions on pth moment stability are also proposed. The main results of this paper allow the estimated upper bound of the diffusion operator associated with the underlying SFDEwMS of the Lyapunov function to have time-varying coefficients (the coefficients may even be sign-changing functions). Examples are provided to illustrate the effectiveness of the proposed results. 相似文献
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Tao Wu Lianglin Xiong Jinde Cao Zixin Liu Haiyang Zhang 《Journal of The Franklin Institute》2018,355(17):8462-8483
This paper discusses the stabilization criteria for stochastic neural networks of neutral type with both Markovian jump parameters. First, delay-dependent conditions to guarantee the globally exponential stability in mean square and almost surely exponential stability of such systems are obtained by combining an appropriate constructed Lyapunov–Krasovskii functional with the semi-martingale convergence theorem. These conditions are in terms of the linear matrix inequalities (LMIs), which can be some less conservative than some existing results. Second, based on the obtained stability conditions, the state feedback controller is designed. Finally, four numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method. 相似文献
9.
Likang Feng Weihai Zhang Zhichun Yang Ju H. Park 《Journal of The Franklin Institute》2021,358(10):5426-5450
In this paper, the global asymptotic stability in probability and the exponential stability in th moment are investigated for random nonlinear systems with stochastic impulses, whose occurrence is determined by a Poisson process. The stochastic disturbances in the impulsive random nonlinear systems are driven by second-order processes, which have bounded mean power. Firstly, the improved Lyapunov approaches for the global asymptotic stability in probability and the exponential stability in th moment are established for impulsive random nonlinear systems based on the uniformly asymptotically stable function. Secondly, the improved results are further extended to the impulsive random nonlinear systems with Markovian switching. Finally, two examples are provided to verify the feasibility and effectiveness of the obtained results. 相似文献
10.
《Journal of The Franklin Institute》2023,360(2):1005-1035
There are many hybrid stochastic differential equations (SDEs) in the real-world that don’t satisfy the linear growth condition (namely, SDEs are highly nonlinear), but they have highly nonlinear characteristics. Based on some existing results, the main difficulties here are to deal with those equations if they are driven by Lévy noise and delay terms, then to investigate their stability in this case. The present paper aims to show how to stabilize a given unstable nonlinear hybrid SDEs with Lévy noise by designing delay feedback controls in the both drift and diffusion parts of the given SDEs. The controllers are based on discrete-time state observations which are more realistic and make the cost less in practice. By using the Lyapunov functional method under a set of appropriate assumptions, stability results of the controlled hybrid SDEs are discussed in the sense of pth moment asymptotic stability and exponential stability. As an application, an illustrative example is provided to show the feasibility of our theorem. The results obtained in this paper can be considered as an extension of some conclusions in the stabilization theory. 相似文献
11.
Bo Zhang Feiqi Deng Shiguo Peng Shengli Xie 《Journal of The Franklin Institute》2018,355(9):3829-3852
This paper considers the stabilization and destabilization of a given nonlinear system by an intermittent Brownian noise perturbation. We give some distinct conditions and conclusions on almost sure exponential stability and instability, which are related to the control period T and the noise width δ. These results are then exploited to examine stabilization and destabilization via intermittent stochastic perturbation and applied to the stabilization of a memristor-based chaotic system. Two numerical examples are presented to illustrate the theoretical results. 相似文献
12.
In this paper, the issue about the stationary distribution for hybrid multi-stochastic-weight coupled networks (HMSWCN) via aperiodically intermittent control is investigated. Specially, when stochastic disturbance gets to zero, the exponential stability in pth moment for hybrid multi-weight coupled networks (HMWCN) is considered. Under the framework of the Lyapunov method, M-matrix and Kirchhoff’s Matrix Tree Theorem in the graph theory, several sufficient conditions are derived to guarantee the existence of a stationary distribution and exponential stability. Different from previous work, the existing area of a stationary distribution is not only related to the topological structure of coupled networks, but also aperiodically intermittent control (the rate of control width and control duration). Subsequently, as an application to theoretical results, a class of hybrid multi-stochastic-weight coupled oscillators is studied. Ultimately, numerical examples are carried out to demonstrate the effectiveness of theoretical results and effects of the control schemes. 相似文献
13.
Xiaolin Li 《Journal of The Franklin Institute》2008,345(7):779-791
In this paper, an adaptive feedback controller is designed to achieve complete synchronization of unidirectionally coupled delayed neural networks with stochastic perturbation. LaSalle-type invariance principle for stochastic differential delay equations is employed to investigate the globally almost surely asymptotical stability of the error dynamical system. An example and numerical simulation are given to demonstrate the effectiveness of the theory results. 相似文献
14.
《Journal of The Franklin Institute》2019,356(18):11561-11580
This paper addresses the robust H∞ filter design problem for a class of uncertain fuzzy neutral stochastic system with time-delay through Takagi–Sugeno (T–S) fuzzy model. By constructing an augmented Lyapunov–Krasovskii functional, some novel delay-dependent stability criteria for uncertain fuzzy neutral stochastic system with time varying delay are obtained in terms of linear matrix inequalities. By using the integral inequality in the neutral stochastic setting combined with delay decomposition approach, the H∞ fuzzy filter is designed to guarantee the corresponding filtering error systems robustly asymptotically stable with a specified H∞ performance index. At last, two numerical examples are presented to show the less conservatism than the previous results. 相似文献
15.
David Castillo Fernández 《Journal of The Franklin Institute》2010,347(10):1814-1824
In this paper the weak exponential stability with decay function of sample path, which are given by mild solution to a class of semilinear stochastic evolution equations, are presented. The analyses consist in using exponential martingale formula, Lyapunov functional and some special inequalities derived for our stability purposes. Two examples are given to illustrate the theory. 相似文献
16.
This paper is concerned with the input-to-state stability (ISS) of impulsive stochastic systems. First, appropriate concepts of stochastic input-to-state stability (SISS) and pth moment input-to-state stability (p-ISS) for the mentioned systems are introduced. Then, we prove that impulsive stochastic systems possessing SISS-Lyapunov functions are uniformly SISS and p-ISS over a certain class of impulse sequences. As a byproduct, a criterion on the uniform global asymptotic stability in probability for the system in isolation (without inputs) is also derived. Finally, we provide a numerical example to illustrate our results. 相似文献
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This work aims to analyze the exponential stability of a non-linear impulsive neutral stochastic delay differential system. In this study, impulse perturbation is considered a delay-dependent state variable. The solution of the delay-dependent impulsive neutral stochastic delay differential system is associated with the solution of the system without impulses. First, we developed a relation connecting the solution of the neutral stochastic delay differential system without impulses and the solution of the corresponding system with impulses. Then, the conditions of the exponential stability of the proposed impulsive system are derived by determining the stability analysis of the respective system without impulse. The numerical approach for the neutral stochastic delay system without impulses is generated using the Euler-Maruyama method and adopted for the corresponding impulsive system. Finally, the achieved theoretical results are illustrated for applying the Malthusian single species neutral stochastic delay population model with immigration impulses. 相似文献
19.
《Journal of The Franklin Institute》2022,359(8):3749-3767
This paper investigates practical stability problem for nonlinear impulsive stochastic delayed systems driven by G-Brownian motion (IGSDSs). Practical stability can describe quantitative properties and qualitative behavior in contrast to traditional Lyapunov stability theory. Based on G-Lyapunov function, Razumikhin-type theorem, G-Itô formula, Burkholder–Davis–Gundy (B-D-G) inequalities I & II and stochastic analysis technique, some new criteria for moment and quasi sure global practical uniform exponential stability of IGSDSs are proposed. Finally, two examples are presented to verify validity of our theoretical results. 相似文献
20.
This paper is devoted to existence and uniqueness of minimal mild super solutions to the obstacle problem governed by integro-partial differential equations. We first study the well-posedness and local Lipschitz regularity of Lp solutions (p?≥?2) to reflected forward-backward stochastic differential equations (FBSDEs) with jump and lower barrier. Then we show that the solutions to reflected FBSDEs provide a probabilistic representation for the mild super solution via a nonlinear Feynman–Kac formula. Finally, we apply the results to study stochastic optimal control/stopping problems. 相似文献