{"title":"用计算机代数求渐近稳定的近似区域:一个实例研究","authors":"S. Prakash, J. Vanualailai, T. Soma","doi":"10.1071/SP02011","DOIUrl":null,"url":null,"abstract":"One of the classical problems in nonlinear control system analysis and design is to find a region of asymptotic stability by the Direct Method of Lyapunov. This paper tentatively shows, via a numercial example, that this problem can be easily solved using Quantifier Elimination (QE). In particular, if the governing equations are described by differential equations containing only polynomials, then the problem can be conveniently solved by a computer algebra software packages such as Qepcad or Redlog. In our case study, we use a simple Lyapunov function and Qepcad to estimate the stability region, and the results are verified by an optimization method based on Lagrange's method.","PeriodicalId":148381,"journal":{"name":"The South Pacific Journal of Natural and Applied Sciences","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2002-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Obtaining approximate region of asymptotic stability by computer algebra: a case study\",\"authors\":\"S. Prakash, J. Vanualailai, T. Soma\",\"doi\":\"10.1071/SP02011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"One of the classical problems in nonlinear control system analysis and design is to find a region of asymptotic stability by the Direct Method of Lyapunov. This paper tentatively shows, via a numercial example, that this problem can be easily solved using Quantifier Elimination (QE). In particular, if the governing equations are described by differential equations containing only polynomials, then the problem can be conveniently solved by a computer algebra software packages such as Qepcad or Redlog. In our case study, we use a simple Lyapunov function and Qepcad to estimate the stability region, and the results are verified by an optimization method based on Lagrange's method.\",\"PeriodicalId\":148381,\"journal\":{\"name\":\"The South Pacific Journal of Natural and Applied Sciences\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2002-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The South Pacific Journal of Natural and Applied Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1071/SP02011\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The South Pacific Journal of Natural and Applied Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1071/SP02011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Obtaining approximate region of asymptotic stability by computer algebra: a case study
One of the classical problems in nonlinear control system analysis and design is to find a region of asymptotic stability by the Direct Method of Lyapunov. This paper tentatively shows, via a numercial example, that this problem can be easily solved using Quantifier Elimination (QE). In particular, if the governing equations are described by differential equations containing only polynomials, then the problem can be conveniently solved by a computer algebra software packages such as Qepcad or Redlog. In our case study, we use a simple Lyapunov function and Qepcad to estimate the stability region, and the results are verified by an optimization method based on Lagrange's method.
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