{"title":"通过平均脉冲估计方法实现具有脉冲延迟的时延系统的同步。","authors":"Biwen Li, Qiaoping Huang","doi":"10.3934/mbe.2024199","DOIUrl":null,"url":null,"abstract":"<p><p>We investigated synchronization of dynamic systems with mixed delays and delayed impulses. Using impulsive control method and the average impulsive interval approach, several Lyapunov sufficient conditions were given for ensuring synchronization in terms of impulsive perturbation and impulsive control, respectively. The derived conditions indicated that delays in continuous dynamical systems were flexible under impulsive perturbation and were not strictly dependent on the size of impulsive delays, and they may have a potential impact on synchronization of the considered system. In addition, applying the proposed concepts of average positive impulsive estimation and average impulsive estimation, we integrated the information in impulsive delay into the rate coefficient to eliminate the limitation of having the same threshold at each impulse point, while the impulsive delay maintained the synchronization effect. This was an improvement on the previous results obtained. Finally, we provided two numerical examples to illustrate the validity of our results.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Synchronization of time-delay systems with impulsive delay via an average impulsive estimation approach.\",\"authors\":\"Biwen Li, Qiaoping Huang\",\"doi\":\"10.3934/mbe.2024199\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>We investigated synchronization of dynamic systems with mixed delays and delayed impulses. Using impulsive control method and the average impulsive interval approach, several Lyapunov sufficient conditions were given for ensuring synchronization in terms of impulsive perturbation and impulsive control, respectively. The derived conditions indicated that delays in continuous dynamical systems were flexible under impulsive perturbation and were not strictly dependent on the size of impulsive delays, and they may have a potential impact on synchronization of the considered system. In addition, applying the proposed concepts of average positive impulsive estimation and average impulsive estimation, we integrated the information in impulsive delay into the rate coefficient to eliminate the limitation of having the same threshold at each impulse point, while the impulsive delay maintained the synchronization effect. This was an improvement on the previous results obtained. Finally, we provided two numerical examples to illustrate the validity of our results.</p>\",\"PeriodicalId\":49870,\"journal\":{\"name\":\"Mathematical Biosciences and Engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Biosciences and Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.3934/mbe.2024199\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Biosciences and Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.3934/mbe.2024199","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Synchronization of time-delay systems with impulsive delay via an average impulsive estimation approach.
We investigated synchronization of dynamic systems with mixed delays and delayed impulses. Using impulsive control method and the average impulsive interval approach, several Lyapunov sufficient conditions were given for ensuring synchronization in terms of impulsive perturbation and impulsive control, respectively. The derived conditions indicated that delays in continuous dynamical systems were flexible under impulsive perturbation and were not strictly dependent on the size of impulsive delays, and they may have a potential impact on synchronization of the considered system. In addition, applying the proposed concepts of average positive impulsive estimation and average impulsive estimation, we integrated the information in impulsive delay into the rate coefficient to eliminate the limitation of having the same threshold at each impulse point, while the impulsive delay maintained the synchronization effect. This was an improvement on the previous results obtained. Finally, we provided two numerical examples to illustrate the validity of our results.
期刊介绍:
Mathematical Biosciences and Engineering (MBE) is an interdisciplinary Open Access journal promoting cutting-edge research, technology transfer and knowledge translation about complex data and information processing.
MBE publishes Research articles (long and original research); Communications (short and novel research); Expository papers; Technology Transfer and Knowledge Translation reports (description of new technologies and products); Announcements and Industrial Progress and News (announcements and even advertisement, including major conferences).