Schauder不动点与中立型随机动力系统的稳定性  

Schauder Fixed Point and Stability of Neutral Stochastic Systems

作　　者：王春生[1] 李永明[2] WANG Chun-sheng;LI Yong-ming(Department of management,South China Institute of Software Engineering.GUS,Guangzhou 510990,China;School of Mathematics&Computer Science,Shangrao Normal University,Shangrao 334001,China)

机构地区：[1]广州大学华软软件学院管理系,广东广州510990 [2]上饶师范学院数学与计算机科学学院,江西上饶334001

出　　处：《控制工程》2020年第11期1956-1961,共6页Control Engineering of China

基　　金：国家自然科学基金资助项目(11461057);广东省自然科学基金资助项目(2016A030313542);广东省普通高校特色创新项目(自然科学版)(2018KTSCX339);2018年广州大学华软软件学院科学研究、教育教学研究项目(ky201801)。

摘　　要：文章利用Schauder不动点方法研究了一类中立型随机动力系统,并给出了该系统零解指数均方稳定的条件。在研究中立型多变时滞随机动力系统的稳定性时,大多数专家采用的都是Lyapunov直接法和Banach不动点方法,Schauder不动点方法还很少见。文章在证明过程中,根据系统多变时滞的特点,配对引入对应的函数来构造算子,相比以往的研究更加灵活。文章第一次尝试通过实例对Lyapunov直接法、Banach不动点方法和Schauder不动点方法在研究随机动力系统稳定性上的优劣进行了比较分析。文章的结果改进和推广了相关文献的结论,详见实例。In this paper,a class of neutral stochastic dynamical systems is studied by using the Schauder fixed point method.The conditions for the exponential mean square stability of the zero solution of the system are given.In the study of the stability of neutral stochastic dynamical systems with time-varying delays,most experts use the Lyapunov direct method and the Banach fixed point method,and the Schauder fixed point method is still rare.In the course of proof,according to the characteristics of the system with variable delay,the pairing is introduced into the corresponding function to construct the operator,which is more flexible than the previous research.The first attempt is made to compare and analyze the advantages and disadvantages of the Lyapunov direct method,the Banach fixed point method and the Schauder fixed point method in the study of the stability of stochastic dynamical systems.The results of this paper improve and generalize the conclusions of relevant literature.

关 键 词：中立型多变时滞随机动力系统 Schauder不动点方法 LYAPUNOV直接法 Banach不动点方法 指数均方稳定性 

分 类 号：O231.3[理学—运筹学与控制论]