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Basic theory and stability analysis for neutral stochastic functional differential equations with pure jumps

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Science China(Information Sciences) 2019年第1期62卷 119-133页

作者： Mengling LI Feiqi DENG xuerong mao Systems Engineering Institute South China University of Technology Department of Statistics and Modelling Science University of Strathclyde

This paper investigates the existence and uniqueness of solutions to neutral stochastic functional differential equations with pure jumps(NSFDEwPJs). The boundedness and almost sure exponential stability are also considered. In general, the classical existence and uniqueness theorem of solutions can be obtained under a local Lipschitz condition and linear growth condition. However, there are many equations that do not obey the linear growth condition. Therefore, our first aim is to establish new theorems where the linear growth condition is no longer required whereas the upper bound for the diffusion operator will play a leading role. Moreover, the pth moment boundedness and almost sure exponential stability are also obtained under some loose conditions. Finally, we present two examples to illustrate the effectiveness of our results.

关键词： neutral term stochastic functional differential equations pure jumps existence and uniqueness theorem stability analysis

Special focus on modeling, analysis and control of stochastic systems

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Science China(Information Sciences) 2018年第7期61卷 104-105页

作者： Feiqi DENG xuerong mao South China University of Technology University of Strathclyde

Every aspect in the fields of engineering,natural science,and social science is affected by random *** systems,as practical mathematical modeling tools,are also frequently subjected to random influences such as extern... 详细信息

关键词： Special focus on modeling analysis and control of stochastic systems

Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps

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Science China(Information Sciences) 2018年第7期61卷 146-160页

作者： Haoyi MO Mengling LI Feiqi DENG xuerong mao School of Applied Mathematics Guangdong University of Technology Systems Engineering Institute South China University of Technology Department of Mathematics and Statistics University of Strathclyde

The exponential stability of trivial solution and numerical solution for neutral stochastic functional differential equations(NSFDEs) with jumps is considered. The stability includes the almost sure exponential stability and the mean-square exponential stability. New conditions for jumps are proposed by means of the Borel measurable function to ensure stability. It is shown that if the drift coefficient satisfies the linear growth condition, the Euler-Maruyama method can reproduce the corresponding exponential stability of the trivial solution. A numerical example is constructed to illustrate our theory.

关键词： neutral stochastic functional differential equations with jumps almost sure exponential stability mean-square exponential stability Euler-Maruyama method

Boundedness and stability of highly nonlinear hybrid neutral stochastic systems with multiple delays

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Science China(Information Sciences) 2019年第10期62卷 133-148页

作者： Mingxuan SHEN Chen FEI Weiyin FEI xuerong mao School of Science Nanjing University of Science and Technology School of Mathematics and Physics Anhui Polytechnic University Glorious Sun School of Business and Management Donghua University Department of Mathematics and Statistics University of Strathclyde

This paper reports the boundedness and stability of highly nonlinear hybrid neutral stochastic differential delay equations(NSDDEs) with multiple delays. Without imposing linear growth condition, the boundedness and exponential stability of the exact solution are investigated by Lyapunov functional *** particular, using the M-matrix technique, the mean square exponential stability is obtained. Finally, three examples are presented to verify our results.

关键词： hybrid delay systems neutral stochastic systems multiple delays highly nonlinear

Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state

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Science China(Information Sciences) 2018年第7期61卷 130-145页

作者： Gongfei SONG Zhenyu LU Bo-Chao ZHENG xuerong mao Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology School of Information and Control Nanjing University of Information Science and Technology School of Electronic and Information Engineering Nanjing University of Information Science and Technology Department of Mathematics and Statistics University of Strathclyde

Although the mean square stabilization of hybrid systems by feedback control based on discretetime observations of state and mode has been studied by several authors since 2013, the corresponding almost sure stabilization problem has received little attention. Recently, mao was the first to study the almost sure stabilization of a given unstable system ˙x(t) = f(x(t)) by a linear discrete-time stochastic feedback control Ax([t/τ ]τ)d B(t)(namely the stochastically controlled system has the form dx(t) = f(x(t))dt +Ax([t/τ ]τ)d B(t)), where B(t) is a scalar Brownian, τ > 0, and [t/τ ] is the integer part of t/τ. In this paper, we consider a much more general problem. That is, we study the almost sure stabilization of a given unstable hybrid system ˙x(t) = f(x(t), r(t)) by nonlinear discrete-time stochastic feedback control u(x([t/τ ]τ), r([t/τ ]τ))d B(t)(so the stochastically controlled system is a hybrid stochastic system of the form dx(t) = f(x(t), r(t))dt + u(x([t/τ ]τ), r([t/τ ]τ))d B(t)), where B(t) is a multi-dimensional Brownian motion and r(t) is a Markov chain.

关键词： Brownian motion Markov chain generalized Itö formula almost sure exponential stability stochastic feedback control

Delay-dependent robust stability of stochastic delay systems with Markovian switching

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控制理论与应用（英文版） 2009年第4期7卷 367-372页

作者： Lirong HUANG xuerong mao Feiqi DENG Department of Mathematics and Statistics University of Strathclyde Glasgow G1 1XH UK College of Automation Science and Engineering South China University of Technology Guangzhou Guangdong 510641 China

In recent years, the stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities （LMIs）, which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.

关键词： Stochastic systems Time delay Markovian switching Delay-dependent stability

Theory and application of stability for stochastic reaction diffusion systems

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Science in China(Series F) 2008年第2期51卷 158-170页

作者： LUO Qi DENG FeiQi mao xuerong BAO JunDong ZHANG YuTian College of Information and Control Nanjing University of Information Science & Technology Nanjing 210044 China College of Automation South China University of Technology Guangzhou 410640 China Department of Statistics and Modelling Science University of-Strathc/yde Glasgow G1 IXH Scotland UK Coilege of Mathematics Science Inner Mongolia Normal'University Huhhot 010000 China College of Mathematics and Physics Nanjing University of Information Science & Technology Nanjing 210044 China

So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding It6 formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the It6 stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probablity, and exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results ob- tained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper.

关键词： stochastic reaction diffusion system stability in probability asymptotic stability in probability exponentialstability in mean square

具有媒体报道的SVIR传染病模型的生存性分析

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数学物理学报:A辑 2023年第5期43卷 1595-1606页

作者：李丹魏凤英毛学荣福州大学数学与统计学院福州350116 福州大学运筹学与控制论福建省高校重点实验室福州350116 思克莱德大学数学与统计系格拉斯哥G11XH

该文研究了具有Logistic增长和媒体报道的饱和发生率的随机SVIR模型.为了研究模型的动力学性质,首先证明了随机模型全局正解的存在唯一性,其次通过构造合适的李雅普诺夫函数,探究疾病持久和灭绝的充分性条件.研究表明:当R^(s)_(0)>1时,... 详细信息

该文研究了具有Logistic增长和媒体报道的饱和发生率的随机SVIR模型.为了研究模型的动力学性质,首先证明了随机模型全局正解的存在唯一性,其次通过构造合适的李雅普诺夫函数,探究疾病持久和灭绝的充分性条件.研究表明:当R^(s)_(0)>1时,疾病长时间持续存在.当R^(e)_(0)<1时,疾病在流行一段时间后灭绝.最后,通过数值模拟验证了以上结论.

关键词：传染病模型疫苗媒体报道持久性与灭绝性平稳分布

离散延迟观测系统状态和离散观测模态的混杂随机时滞系统的反馈镇定问题

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东华大学学报（自然科学版） 2022年第1期48卷 118-126页

作者：王思敏陆见秋毛学荣东华大学理学院上海201620 思克莱德大学数学与统计系格拉斯哥G11XT

为降低控制成本,同时考虑到现实中的反馈控制信号通常带有延迟,研究了带有马尔可夫切换的非线性连续时间变时滞系统的镇定问题,设计了一种状态和模态离散观测并带有状态延迟的反馈控制器。通过构造有效的Lyapunov泛函,给出了系统在均方... 详细信息

为降低控制成本,同时考虑到现实中的反馈控制信号通常带有延迟,研究了带有马尔可夫切换的非线性连续时间变时滞系统的镇定问题,设计了一种状态和模态离散观测并带有状态延迟的反馈控制器。通过构造有效的Lyapunov泛函,给出了系统在均方意义下H_(∞)稳定、渐近稳定和指数稳定的充分条件,得到含延迟观测时间间隔的上界。最后给出一个数值算例说明所得结论的有效性。

关键词：混杂随机时滞系统反馈控制镇定性状态和模态离散观测 Lyapunov泛函 H_(∞)稳定渐近稳定指数稳定