{"title":"On Uniform Convergence Property of Solutions for Periodic Differential Inclusions with Asymptotically Stable Sets","authors":"M. Morozov","doi":"10.25728/ASSA.2021.21.1.1037","DOIUrl":null,"url":null,"abstract":"The paper considers a periodic differential inclusion with an asymptotically stable set. The uniform character of convergence of solutions to an asymptotically stable set is established. An exponential estimate is obtained for solutions of a periodic differential inclusion homogeneous in state vector. Examples of control systems leading to consideration of periodic differential inclusions are given. These results can find applications in the stability analysis of control systems with periodic parameters, in particular, servomechanisms whose elements operate on AC, control systems with pulse amplitude modulation, and systems used to solve problems related to investigating vibrations of milling machines.","PeriodicalId":39095,"journal":{"name":"Advances in Systems Science and Applications","volume":"21 1","pages":"76-85"},"PeriodicalIF":0.0000,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Systems Science and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.25728/ASSA.2021.21.1.1037","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
The paper considers a periodic differential inclusion with an asymptotically stable set. The uniform character of convergence of solutions to an asymptotically stable set is established. An exponential estimate is obtained for solutions of a periodic differential inclusion homogeneous in state vector. Examples of control systems leading to consideration of periodic differential inclusions are given. These results can find applications in the stability analysis of control systems with periodic parameters, in particular, servomechanisms whose elements operate on AC, control systems with pulse amplitude modulation, and systems used to solve problems related to investigating vibrations of milling machines.
期刊介绍：
Advances in Systems Science and Applications (ASSA) is an international peer-reviewed open-source online academic journal. Its scope covers all major aspects of systems (and processes) analysis, modeling, simulation, and control, ranging from theoretical and methodological developments to a large variety of application areas. Survey articles and innovative results are also welcome. ASSA is aimed at the audience of scientists, engineers and researchers working in the framework of these problems. ASSA should be a platform on which researchers will be able to communicate and discuss both their specialized issues and interdisciplinary problems of systems analysis and its applications in science and industry, including data science, artificial intelligence, material science, manufacturing, transportation, power and energy, ecology, corporate management, public governance, finance, and many others.
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