{"title":"On the Partial Stability in the Probability of Nonlinear Stochastic Functional-Differential Systems with Aftereffect (Delay)","authors":"V. I. Vorotnikov, Yu. G. Martyshenko","doi":"10.1134/s1064230724700011","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A system of nonlinear functional-differential equations with aftereffect (delay) subjected to random processes of “white” noise is considered. It is assumed that the system admits a partial (with respect to some part of the state variables) zero equilibrium position. The problem of the stability in the probability of the given equilibrium position is posed, and stability is considered not for all variables but for some of the variables that determine this equilibrium position. For the solution of this problem, a stochastic version of the method of Lyapunov–Krasovskii functionals is used with the appropriated specification of the requirements for the functionals. In order to expand the capabilities of the method used, it is also proposed to correct the domain of the functional space in which auxiliary Lyapunov–Krasovskii functionals are constructed. The conditions for partial stability of this type are obtained. Examples are given that show the features of the proposed approach.</p>","PeriodicalId":50223,"journal":{"name":"Journal of Computer and Systems Sciences International","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computer and Systems Sciences International","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1134/s1064230724700011","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
A system of nonlinear functional-differential equations with aftereffect (delay) subjected to random processes of “white” noise is considered. It is assumed that the system admits a partial (with respect to some part of the state variables) zero equilibrium position. The problem of the stability in the probability of the given equilibrium position is posed, and stability is considered not for all variables but for some of the variables that determine this equilibrium position. For the solution of this problem, a stochastic version of the method of Lyapunov–Krasovskii functionals is used with the appropriated specification of the requirements for the functionals. In order to expand the capabilities of the method used, it is also proposed to correct the domain of the functional space in which auxiliary Lyapunov–Krasovskii functionals are constructed. The conditions for partial stability of this type are obtained. Examples are given that show the features of the proposed approach.
期刊介绍：
Journal of Computer and System Sciences International is a journal published in collaboration with the Russian Academy of Sciences. It covers all areas of control theory and systems. The journal features papers on the theory and methods of control, as well as papers devoted to the study, design, modeling, development, and application of new control systems. The journal publishes papers that reflect contemporary research and development in the field of control. Particular attention is given to applications of computer methods and technologies to control theory and control engineering. The journal publishes proceedings of international scientific conferences in the form of collections of regular journal articles and reviews by top experts on topical problems of modern studies in control theory.
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