{"title":"Absolute stability analysis of multivariable regulators through the Popov criterion","authors":"J. D. da Cruz, J. Geromel","doi":"10.1109/CDC.1988.194721","DOIUrl":null,"url":null,"abstract":"The multivariable Popov criterion is used to derive the sectors of absolute stability for two classes of regulators in both the continuous and discrete-time cases. The first class corresponds to the well known linear quadratic regulators; in the second one a feedback control law depending on the solution of a Lyapunov equation is considered. Relatively simple reasoning shows that the absolute stability analysis can be accomplished in the frequency domain. To carry this out, necessary conditions for a given matrix transfer function to represent a specific regulator are established. It is shown that the necessary conditions play the same role in the absolute stability context as the Kalman frequency-domain equality does with respect to stability margins.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"75 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 27th IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1988.194721","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The multivariable Popov criterion is used to derive the sectors of absolute stability for two classes of regulators in both the continuous and discrete-time cases. The first class corresponds to the well known linear quadratic regulators; in the second one a feedback control law depending on the solution of a Lyapunov equation is considered. Relatively simple reasoning shows that the absolute stability analysis can be accomplished in the frequency domain. To carry this out, necessary conditions for a given matrix transfer function to represent a specific regulator are established. It is shown that the necessary conditions play the same role in the absolute stability context as the Kalman frequency-domain equality does with respect to stability margins.<>
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