{"title":"奇异振动系统的鲁棒最小范数部分特征值分配","authors":"Kang Zhao, Jiantian Wang, Fangting Deng","doi":"10.1016/j.jmaa.2025.130048","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, the partial quadratic eigenvalue assignment problem (PQEAP) for the singular second-order system by the acceleration-velocity-displacement active controller was considered. Based on the spectral decomposition of quadratic symmetric pencil, a sufficient and necessary condition of the closed-loop to preserve no spill-over is provided. Using the receptances and system matrices, the parametric solutions of the PQEAP are characterized. Finally, a gradient-based optimization algorithm for the robust and minimum norm solution of the PQEAP is proposed. Numerical examples show the robustness and effectiveness of the proposed method.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130048"},"PeriodicalIF":1.2000,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Robust and minimum norm partial eigenvalue assignment in singular vibration systems\",\"authors\":\"Kang Zhao, Jiantian Wang, Fangting Deng\",\"doi\":\"10.1016/j.jmaa.2025.130048\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, the partial quadratic eigenvalue assignment problem (PQEAP) for the singular second-order system by the acceleration-velocity-displacement active controller was considered. Based on the spectral decomposition of quadratic symmetric pencil, a sufficient and necessary condition of the closed-loop to preserve no spill-over is provided. Using the receptances and system matrices, the parametric solutions of the PQEAP are characterized. Finally, a gradient-based optimization algorithm for the robust and minimum norm solution of the PQEAP is proposed. Numerical examples show the robustness and effectiveness of the proposed method.</div></div>\",\"PeriodicalId\":50147,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Applications\",\"volume\":\"555 1\",\"pages\":\"Article 130048\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022247X25008297\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25008297","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Robust and minimum norm partial eigenvalue assignment in singular vibration systems
In this paper, the partial quadratic eigenvalue assignment problem (PQEAP) for the singular second-order system by the acceleration-velocity-displacement active controller was considered. Based on the spectral decomposition of quadratic symmetric pencil, a sufficient and necessary condition of the closed-loop to preserve no spill-over is provided. Using the receptances and system matrices, the parametric solutions of the PQEAP are characterized. Finally, a gradient-based optimization algorithm for the robust and minimum norm solution of the PQEAP is proposed. Numerical examples show the robustness and effectiveness of the proposed method.
期刊介绍:
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Papers are sought which employ one or more of the following areas of classical analysis:
• Analytic number theory
• Functional analysis and operator theory
• Real and harmonic analysis
• Complex analysis
• Numerical analysis
• Applied mathematics
• Partial differential equations
• Dynamical systems
• Control and Optimization
• Probability
• Mathematical biology
• Combinatorics
• Mathematical physics.