Mean-square exponential stability of stochastic Volterra systems in infinite dimensions  

作　　者：Lin FU Shiguo PENG Feiqi DENG Quanxin ZHU 

机构地区：[1]School of Automation,Guangdong University of Technology,Guangzhou 510006,China [2]School of Automation Science andEngineering,South China University ofTechnology,Guangzhou 510006,China [3]Key Laboratory of Computing and Stochastic Mathematics Ministry of Education,School of Mathematics and Statistics,Hunan Normal University,Changsha 410081,China

出　　处：《Science China(Information Sciences)》2024年第10期294-310,共17页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61973092,62073144,62333006,62173139);Science and Technology Innovation Program of Hunan Province(Grant No.2021RC4030)。

摘　　要：Over the past decade,the study of stability theory in integro-differential systems has grown significantly owing to their relevance in solving physical and engineering problems,such as viscoelasticity and thermo-viscoelasticity in materials with memory properties.This paper concentrates on a class of infinite-dimensional stochastic integro-differential systems.We establish the well-posedness of the system and identify mild solutions to the system and an abstract stochastic Cauchy problem.This identification is identified by employing a semigroup approach combined with Yosida approximation.We derive sufficient conditions that ensure the mean-square exponential stability of mild solutions to the system boils down to the boundedness of a certain function and a norm estimate for the stochastic part.These conditions are implemented through the semigroup approach and the composition operator method.Illustrative examples are provided and the obtained theoretical results are validated by numerical simulations.

关 键 词：stochastic integro-differential equations mean-square exponential stability stochastic distributed parameter systems Hardy space composition operators 

分 类 号：O211.6[理学—概率论与数理统计]