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This paper is concerned with exponential stability for a class of generalized stochastic impulsive functional differential equations with delayed impulses and Markovian switching. A novel subsequence approach of the impulsive and ...
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This paper is concerned with exponential stability for a class of generalized stochastic impulsive functional differential equations with delayed impulses and Markovian switching. A novel subsequence approach of the impulsive and switching time sequence is introduced to cope with the impulsive control problem with large and small delays. Based on the stochastic Lyapunov function and Razumikhin technique, a dwell time bound and related criteria are established to ensure the pth moment exponential stability, almost surely exponential stability and uniform stability of the trivial solutions. The main advantage of the proposed algorithm lies in that the delay bound and parameters are not necessarily required, which are commonly used to restrict the dwell-time bound and the decay rate of Lyapunov function. Finally, two examples are performed to demonstrate the usefulness of the main results. Keywords: Impulsive systems Delayed impulses Markovian switching (C) 2018 Elsevier Ltd. All rights reserved.
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In this paper, we analyze a stochastic Gilpin-Ayala population model with Markovian switching and white noise. The Gilpin-Ayala parameter is also allowed to switch. We establish the global stability of the trivial equilibrium stat...
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In this paper, we analyze a stochastic Gilpin-Ayala population model with Markovian switching and white noise. The Gilpin-Ayala parameter is also allowed to switch. We establish the global stability of the trivial equilibrium state of the model. Verifiable sufficient conditions which guarantee the extinction and persistence are provided. Furthermore, we show the existence of a stationary distribution. The analytical results are illustrated by computer simulations. (C) 2015 Elsevier Ireland Ltd. All rights reserved.
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A more general class of stochastic nonlinear systems with irreducible homogenous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first pr...
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A more general class of stochastic nonlinear systems with irreducible homogenous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a Lyapunov function. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded-in-probability solution in the biased case.
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The problem of the adaptive tracking for a class of stochastic nonlinear systems with stationary Markovian switching is considered in this note. An Ito formula is proposed for stochastic integral equations with an integral about m...
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The problem of the adaptive tracking for a class of stochastic nonlinear systems with stationary Markovian switching is considered in this note. An Ito formula is proposed for stochastic integral equations with an integral about martingale measure. An adaptive backstepping controller is designed such that the closed-loop system has a unique solution that is globally bounded in probability and $L_4$ -norm of the tracking error converges to an arbitrarily small neighborhood of zero. A simulation example demonstrates the efficiency of the proposed scheme.
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In this paper, the asymptotic stabilization problem is investigated for a class of switched stochastic systems with semi-Markovian switching signals and actuator saturation. By using the stochastic analysis theory and multiple Lya...
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In this paper, the asymptotic stabilization problem is investigated for a class of switched stochastic systems with semi-Markovian switching signals and actuator saturation. By using the stochastic analysis theory and multiple Lyapunov function method, sufficient conditions for the local asymptotic mean square stability of the related system are established based on the stationary distribution of the embedded Markov chain. Moreover, the mode-dependent state feedback controller and estimation of domain of attraction in mean square sense are proposed in terms of a family of decoupled linear matrix inequalities (LMIs). Finally, two examples are provided to illustrate the effectiveness of the proposed results. (C) 2019 Elsevier Inc. All rights reserved.
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This paper is concerned with the robust H filter design for a class of uncertain singular time-delayed Markovian jump systems, whose transition rate matrix has elementwise bounded uncertainties. By the LMI approach, a novel bounde...
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This paper is concerned with the robust H filter design for a class of uncertain singular time-delayed Markovian jump systems, whose transition rate matrix has elementwise bounded uncertainties. By the LMI approach, a novel bounded real lemma is proposed such that the singular Markovian jump system is robustly exponentially mean-square admissible with a prescribed H performance index. Based on this, a sufficient condition for the existence of a robust H filter is developed in terms of LMIs. Finally, a numerical example is provided to show the effectiveness of the theoretical results. Copyright (c) 2013 John Wiley & Sons, Ltd.
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This paper is concerned with a finite-horizon optimal selling rule. A set of geometric Brownian motions coupled by a finite-state Markov chain is used to characterize stock price movements. Given a fixed transaction fee, the optim...
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This paper is concerned with a finite-horizon optimal selling rule. A set of geometric Brownian motions coupled by a finite-state Markov chain is used to characterize stock price movements. Given a fixed transaction fee, the optimal selling rule can be obtained by solving an optimal stopping problem. The corresponding value function is shown to be the unique viscosity solution to the associated HJB equations. Numerical solutions to these equations and their convergence are obtained. A numerical example is presented to illustrate the results. (c) 2005 Elsevier Inc. All rights reserved.
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In this paper, the pth moment stability of hybrid stochastic differential equations is investigated. Several new sufficient conditions are derived by constructing an auxiliary delayed differential equation and using the comparison...
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In this paper, the pth moment stability of hybrid stochastic differential equations is investigated. Several new sufficient conditions are derived by constructing an auxiliary delayed differential equation and using the comparison principle. The proposed criteria remove some harsh restrictions imposed on the diffusion operators and improve some previous related works. Numerical examples and simulations are given to illustrate the effectiveness of theoretical results. (C) 2016 Elsevier Inc. All rights reserved.
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Taking into account of both white and colored noises, a stochastic epidemic model with nonlinear incident rate under regime switching is formulated. Based on this model, we investigate the dynamic behaviors such as ergodicity and ...
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Taking into account of both white and colored noises, a stochastic epidemic model with nonlinear incident rate under regime switching is formulated. Based on this model, we investigate the dynamic behaviors such as ergodicity and extinction of the SIR model with Beddington-DeAngelis incidence rate and Markov switching. First, we study the existence of the unique positive solution of system (1.3). Secondly, by using Lyapunov functions, we prove that the system has a ergodic stationary distribution under certain sufficient conditions. Then, we obtain the conditions for extinction. Finally, numerical simulations are employed to illustrate our theoretical analysis. (C) 2018 Elsevier B.V. All rights reserved.
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In this paper, by using the Lyapunov stability theory, Dynkin's formula, matrix theory, neutral differential equations theory and stochastic analysis techniques, we study the pth moment exponential stability for neutral stochastic...
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In this paper, by using the Lyapunov stability theory, Dynkin's formula, matrix theory, neutral differential equations theory and stochastic analysis techniques, we study the pth moment exponential stability for neutral stochastic delay differential equations (NSDDEs) with Markovian switching, p >= 1. Some new conditions are derived to obtain the pth moment exponential stability of the trivial solution. At last, an example is presented to show the effectiveness of the proposed results. (C) 2015 Elsevier Ltd. All rights reserved.
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