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Theory and application of stability for stochastic reaction diffusion systems

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

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On stabilization for a class of nonlinear stochastic time-delay systems:a matrix inequality approach

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控制理论与应用（英文版） 2006年第3期4卷 229-234页

作者： Weihai ZHANG Xuezhen LIU Shulan KONG Qinghua LI College of Information and Electrical Engineering S handong University of Science and Technology Qingdao Shandong 266510 China School of Electronic Information and Control Engineering Shandong Institute of Light Industry Jinan Shandong 250100 China School of Mathematics Sciences Qufu Normal University Qufu Shandong 273165 China

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.

关键词： Nonlinear stochastic systems Linear matrix inequality asymptotic stability in probability Time-delay systems

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stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility

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Journal of Applied Mathematics and Physics 2024年第2期12卷 509-532页

作者： Modeste N’zi Boubacar Sidiki Kouyaté Ilimidi Yattara Modibo Diarra Laboratory of Applied Mathematics and Computer Science University Felix Houphouet-Boigny Abidjan C&#244te d’Ivoire Department of Mathematics and Computer Science University of Science Technic and Technologies Bamako Mali

In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R0 ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.

关键词： SIRS Delayed Epidemic Model Nonlinear Incidence rate Lyapunov Function asymptotic stability in probability

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State Feedback Stabilization of Nonlinear Stochastic Systems

State Feedback Stabilization of Nonlinear Stochastic Systems

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第二十六届中国控制会议

作者： Zhang Weihai1,2,Yan Zhiguo 1 1.School of Electronic Information and Control Engineering,Shandong Institute of Light Industry,Jinan 250353,P.R.China2.College of Information and Electrical Engineering,Shandong University of Science and Technology,Qingdao 266510,P.R.China

This paper studies the feedback stabilization of nonlinear affine stochastic systems,for which,sufficient conditions for the locally and globally asymptotic stabilization in probability are presented by means of Hamilton-Jacobi inequalities （HJIs）.As corollaries,some previous results are *** example is given to show the validity of the developed theory.

关键词： asymptotic stability in probability Hamilton-Jacobi inequality Feedback stabilization

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