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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

Stability of neutral stochastic differential equations

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Chinese Science Bulletin 1997年第13期42卷 1143-1144页

作者： LIAO Xiaoxi and mao xuerong1 Department of Automatic Control, Huazhong University of Science and Technology, Wuhan 430074, China 2 Department of Statistics and Modelling Science, University of Strathclyde GL LXH, U K.

Let ω（t） = （ω1（t）,…, ωm（t））T be a Brownian motion defined on a complete probabili-ty space （Ω, F, P）. τ>0, A, B, C are n×n matrices. σ: R+×Rn×Rn→Rn×n, whichis locally Lipschitz continuous and satisfies the linear growth condition. Theorem 1. Assume that there exists a symmetric nonnegative n×n matrix D such thatthe symmetric

关键词： root

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混杂随机微分方程理论概述

南京信息工程大学学报（自然科学版） 2017年第3期9卷 246-261页

作者：毛学荣斯特莱斯克莱德大学

本文对混杂随机时滞微分方程的当前发展及最新的研究成果进行了概述.主要回顾了混杂随机微分方程解的存在唯一性定理、稳定性、鲁棒有界性以及离散时间反馈镇定性等部分对混杂随机微分方程的研究起到关键推动作用的成果.

关键词：布朗运动马尔科夫链存在唯一性稳定性反馈控制镇定