{"title":"离散多项式多边形的鲁棒稳定性定理","authors":"J. Peterson, L. Pujara","doi":"10.1109/ICSYSE.1991.161135","DOIUrl":null,"url":null,"abstract":"How to partition an unstable polytope of polynomials into stable and unstable regions is addressed. L.R. Pujara and N. Shanghag have taken the first step by proposing a partition algorithm for unstable polygons of continuous polynomials. The present study begins with a discrete version of the segment lemma of H. Chapellat and S.P. Battacharyya (1989). Some necessary and sufficient conditions are proven for a polynomial vanishing at e* (where *=J omega /sub 0/), for some omega /sub 0/, in a polygon of discrete polynomials. These results lead directly to a method for partitioning polygons of discrete polynomials.<<ETX>>","PeriodicalId":250037,"journal":{"name":"IEEE 1991 International Conference on Systems Engineering","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Some robust stability theorems for polygons of discrete polynomials\",\"authors\":\"J. Peterson, L. Pujara\",\"doi\":\"10.1109/ICSYSE.1991.161135\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"How to partition an unstable polytope of polynomials into stable and unstable regions is addressed. L.R. Pujara and N. Shanghag have taken the first step by proposing a partition algorithm for unstable polygons of continuous polynomials. The present study begins with a discrete version of the segment lemma of H. Chapellat and S.P. Battacharyya (1989). Some necessary and sufficient conditions are proven for a polynomial vanishing at e* (where *=J omega /sub 0/), for some omega /sub 0/, in a polygon of discrete polynomials. These results lead directly to a method for partitioning polygons of discrete polynomials.<<ETX>>\",\"PeriodicalId\":250037,\"journal\":{\"name\":\"IEEE 1991 International Conference on Systems Engineering\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE 1991 International Conference on Systems Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICSYSE.1991.161135\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE 1991 International Conference on Systems Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICSYSE.1991.161135","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Some robust stability theorems for polygons of discrete polynomials
How to partition an unstable polytope of polynomials into stable and unstable regions is addressed. L.R. Pujara and N. Shanghag have taken the first step by proposing a partition algorithm for unstable polygons of continuous polynomials. The present study begins with a discrete version of the segment lemma of H. Chapellat and S.P. Battacharyya (1989). Some necessary and sufficient conditions are proven for a polynomial vanishing at e* (where *=J omega /sub 0/), for some omega /sub 0/, in a polygon of discrete polynomials. These results lead directly to a method for partitioning polygons of discrete polynomials.<>
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