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Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations

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Science China Mathematics 2017年第4期60卷 735-744页

作者： YUE Chao School of Economics and Trade Zhengzhou University of Aeronautics Zhengzhou 450015 China

We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with real parameters. When 0 ≥ 3/2, the improved split-step theta methods can reproduce the mean-square stability of the linear test equations for any step sizes h 〉 0. Then, under a coupled condition on the drift and diffusion coefficients, we consider exponential mean-square stability of the method for nonlinear non-autonomous stochastic differential equations. Finally, the obtained results are supported by numerical experiments.

关键词： stochastic differential equations mean-square stability improved split-step theta methods expo-nential mean-square stability

mean-square stability and Feedback Stabilization of Linear Stochastic System with Distributed Parameter

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Mean-Square Stability and Feedback Stabilization of Linear S...

mean square stability of recurrent neural networks with random delay and Markovian switching

第二十四届中国控制会议

作者： Song Yanan~1, Deng Feiqi~2, Luo Qi~3, Yang Yimin~1 (1. College of Automation, Guangdong University of Technology Guangdong Guangzhou, China P.R.510090) (2. College of Automation Science and Engineering of South China University of Technology, Guangzhou, China P. R. 510640) (3. College of Science, Wu Han University of Science and Technology, Wu Han 430081)

＜正＞ In this paper, mean-square stability and feedback stabilization of linear stochastic system with distributed parameter are discussed. Main idea of this paper is to translate partial differential equations into ordinary differential equations considering boundary condition and Green formula. Sufficient criteria and method of feedback stabilization of this class of systems are given. Simulation is given at the end of this paper.

关键词： Delay Distributed parameter mean-square stability Ito formula

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Journal of Harbin Institute of Technology(New Series) 2009年第5期16卷 678-682页

作者：朱恩文王勇张汉君邹捷中 School of Mathematics and Computational Science Changsha University of Science and Technology School of Mathematics and Computational Science Xiangtan University Dept.of Mathematics Harbin Institute of Technology School of Mathematics Central South University

To establish easily proved conditions under which the random delayed recurrent neural network with Markovian switching is mean-square stability,the evolution of the delay was modeled by a continuous-time homogeneous Markov process with a finite number of *** employing Lyapunov-Krasovskii functionals and conducting stochastic analysis,a linear matrix inequality (LMI) approach was developed to derive the criteria for mean-square stability,which can be readily checked by some standard numerical packages such as the Matlab LMI Toolbox.A numerical example was exploited to show the usefulness of the derived LMI-based stability conditions.

关键词： recurrent neural networks mean-square stability random delay Markovian switching linear matrix inequality

The Data-Reusing MCC-Based Algorithm and Its Performance Analysis

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Chinese Journal of Electronics 2016年第4期25卷 719-725页

作者： LIU Chunhui QI Yue DING Wenrui Research Institute of Unmanned Aerial Vehicle Beihang University State Key Laboratory of Virtual Reality Technology and System Beihang University

Maximum correntropy criterion(MCC)provides a robust optimality criterion for non-Gaussian signal *** this paper,the weight update equation of the conventional MCC-based adaptive filtering algorithm is modified by reusing the past K input vectors,forming a class of data-reusing MCC-based algorithm,called DRMCC *** with the conventional MCCbased algorithm,the DR-MCC algorithm provides a much better convergence performance when the input data is *** mean-square stability bound of the DRMCC algorithm has been studied *** both Gaussian noise case and non-Gaussian noise case,the expressions for the steady-state Excess mean square error(EMSE) of DR-MCC algorithm have been *** relationship between the data-reusing order and the steadystate EMSEs is also *** results are in agreement with the theoretical analysis.

关键词： Adaptive filtering Maximum correntropy criterion(MCC) Data-reusing mean-square stability Steady-state excess mean square error

Global synchronization of general delayed complex networks with stochastic disturbances

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Chinese Physics B 2011年第3期20卷 74-80页

作者：涂俐兰 Hubei Province Key Laboratory of Systems Science in Metallurgical Process Wuhan University of Science and Technology

In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, Ito＇s differential rule and the linear matrix inequality （LMI） optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions.

关键词： global synchronization general delayed complex networks with stochastic disturbances linear matrix inequality mean-square stability

A NOTE ON stability OF THE SPLIT-STEP BACKWARD EULER METHOD FOR LINEAR STOCHASTIC DELAY INTEGRO-DIFFERENTIAL EQUATIONS

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Journal of Systems Science & Complexity 2012年第5期25卷 873-879页

作者： Feng JIANG Yi SHEN Xiaoxin LIAO Department of Control Science and Engineering Huazhong University of Science and Technology School of Statistics and Mathematics Zhongnan University of Economics and Law Department of Control Science and Engineering the Key Laboratory of Ministry of Eduction for Image Processing and Intelligent ControlHuazhong University of Science and Technology

In the literature （Tan and Wang, 2010）, Tan and Wang investigated the convergence of the split-step backward Euler （SSBE） method for linear stochastic delay integro-differential equations （SDIDEs） and proved the mean-square stability of SSBE method under some condition. Unfortu- nately, the main result of stability derived by the condition is somewhat restrictive to be applied for practical application. This paper improves the corresponding results. The authors not only prove the mean-square stability of the numerical method but also prove the general mean-square stability of the numerical method. Furthermore, an example is given to illustrate the theory.

关键词： General mean-square stability mean-square stability split-step backward Euler method stochastic delay integro-differential equations.

On Stabilization of It Stochastic Time-Varying Systems

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Journal of Systems Science & Complexity 2017年第4期30卷 818-827页

作者： GAO Rong ZHANG Huanshui School of Control Science and Engineering Shandong UniversityJinan 250061China School of Mathematics and Statistics Science Ludong UniversityYantai 264025China

The stabilization with receding horizon control （RHC） of It5 stochastic time-varying systems is studied in this paper. Based on monotonically non-increasing of optimal cost and stochastic Lyapunov stability theory, a necessary and sufficient stabilization condition on the terminal weighting matrix is proposed, which guarantees the mean-square stability of the closed-loop system. The explicit receding horizon controller is obtained by employing stochastic maximum principle. Simulations demonstrate the effectiveness of the proposed method.

关键词： mean-square stability receding horizon control stochastic time-varying system.

Novel delay-distribution-dependent stability analysis for continuous-time recurrent neural networks with stochastic delay

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Chinese Physics B 2012年第12期21卷 161-167页

作者：王申全冯健赵青 College of Information Science and Engineering Northeastern University Department of Electrical and Computer Engineering University of Alberta

In this paper, the problem of delay-distribution-dependent stability is investigated for continuous-time recurrent neural networks （CRNNs） with stochastic delay. Different from the common assumptions on time delays, it is assumed that the probability distribution of the delay taking values in some intervals is known a priori. By making full use of the information concerning the probability distribution of the delay and by using a tighter bounding technique （the reciprocally convex combination method）, less conservative asymptotic mean-square stable sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. Two numerical examples show that our results are better than the existing ones.

关键词： recurrent neural networks stochastic delay mean-square stability linear matrix inequal- ity

A necessary and sufficient stabilization condition for discrete time-varying stochastic systems with multiplicative noise

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Control Theory and Technology 2016年第2期14卷 151-158页

作者： Rong GAO Xiaohua LIU Huanshui ZHANG School of Control Science and Engineering Shandong University Jinan Shandong 250061 China School of Mathematics and Statistics Science Ludong University Yantai Shandong 264025 China

This paper investigates a fundamental problem of stabilization for time-varying multiplicative noise stochastic systems. A necessary and sufficient stabilization condition is presented based on the receding horizon approach. The explicit time-varying controller is designed if the condition is satisfied. The presented results are new to the best of our knowledge.

关键词： Receding horizon control time-varying stochastic system mean-square stability multiplicative noise