{"title":"多模多维系统与泊松测序","authors":"Erik I. Verriest","doi":"10.4310/CIS.2009.V9.N1.A4","DOIUrl":null,"url":null,"abstract":"The dynamics of hybrid systems with mode dynamics of different dimensions is described. The first part gives some deterministic examples of such multi-mode multi-dimensional (M 3 D) systems. The second part considers such models under sequential switching at random times. More specifically, the backward Kolmogorov equation is derived, and Lie-algebraic methods are used in the case where the modes are linear. For Poissonian switched equi-dimensional modes, the dif- fusion limit and its implication in vibrational stability are studied. The motion of a pebble on an elevator belt is given as an example.","PeriodicalId":185710,"journal":{"name":"Commun. Inf. Syst.","volume":"98 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Multi-Mode Multi-Dimensional Systems with Poissonian Sequencing\",\"authors\":\"Erik I. Verriest\",\"doi\":\"10.4310/CIS.2009.V9.N1.A4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The dynamics of hybrid systems with mode dynamics of different dimensions is described. The first part gives some deterministic examples of such multi-mode multi-dimensional (M 3 D) systems. The second part considers such models under sequential switching at random times. More specifically, the backward Kolmogorov equation is derived, and Lie-algebraic methods are used in the case where the modes are linear. For Poissonian switched equi-dimensional modes, the dif- fusion limit and its implication in vibrational stability are studied. The motion of a pebble on an elevator belt is given as an example.\",\"PeriodicalId\":185710,\"journal\":{\"name\":\"Commun. Inf. Syst.\",\"volume\":\"98 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Commun. Inf. Syst.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/CIS.2009.V9.N1.A4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Commun. Inf. Syst.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/CIS.2009.V9.N1.A4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Multi-Mode Multi-Dimensional Systems with Poissonian Sequencing
The dynamics of hybrid systems with mode dynamics of different dimensions is described. The first part gives some deterministic examples of such multi-mode multi-dimensional (M 3 D) systems. The second part considers such models under sequential switching at random times. More specifically, the backward Kolmogorov equation is derived, and Lie-algebraic methods are used in the case where the modes are linear. For Poissonian switched equi-dimensional modes, the dif- fusion limit and its implication in vibrational stability are studied. The motion of a pebble on an elevator belt is given as an example.
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