{"title":"脉冲系统平衡位置稳定的充分条件","authors":"O. Anashkin, O. Yusupova","doi":"10.1109/STAB49150.2020.9140587","DOIUrl":null,"url":null,"abstract":"Impulsive differential equations demonstrate rather more complex behavior of solutions than ordinary differential equations. This complexity is due to discontinuities of the integral curves at the moments of impulse actions. We consider a periodic impulsive system in the critical case, when the monodromy matrix of the linear approximation of the system at an equilibrium point has a pair of complex conjugate multipliers on the unit circle. An algorithm for computing of the first Lyapunov value is proposed.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Sufficient conditions for stability of the equilibrium position of an impulsive system\",\"authors\":\"O. Anashkin, O. Yusupova\",\"doi\":\"10.1109/STAB49150.2020.9140587\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Impulsive differential equations demonstrate rather more complex behavior of solutions than ordinary differential equations. This complexity is due to discontinuities of the integral curves at the moments of impulse actions. We consider a periodic impulsive system in the critical case, when the monodromy matrix of the linear approximation of the system at an equilibrium point has a pair of complex conjugate multipliers on the unit circle. An algorithm for computing of the first Lyapunov value is proposed.\",\"PeriodicalId\":166223,\"journal\":{\"name\":\"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)\",\"volume\":\"46 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/STAB49150.2020.9140587\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/STAB49150.2020.9140587","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Sufficient conditions for stability of the equilibrium position of an impulsive system
Impulsive differential equations demonstrate rather more complex behavior of solutions than ordinary differential equations. This complexity is due to discontinuities of the integral curves at the moments of impulse actions. We consider a periodic impulsive system in the critical case, when the monodromy matrix of the linear approximation of the system at an equilibrium point has a pair of complex conjugate multipliers on the unit circle. An algorithm for computing of the first Lyapunov value is proposed.
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