Stability and Performance of First-Order Linear Time-Delay Feedback Systems: An Eigenvalue Approach
Linear time-delay systems with transcendental characteristic equations have infinitely many eigenvalues which are generally hard to compute completely. However, the spectrum of first-order linear time-delay systems can be analyzed with the Lambert function. This paper studies the stability and state...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Control Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2011/719730 |
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| _version_ | 1832561007332950016 |
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| author | Shu-An He I-Kong Fong |
| author_facet | Shu-An He I-Kong Fong |
| author_sort | Shu-An He |
| collection | DOAJ |
| description | Linear time-delay systems with transcendental characteristic equations have infinitely many eigenvalues which are generally hard to compute completely. However, the spectrum of first-order linear time-delay systems can be analyzed with the Lambert function. This paper studies the stability and state feedback stabilization of first-order linear time-delay system in detail via the Lambert function. The main issues concerned are the rightmost eigenvalue locations, stability robustness with respect to delay time, and the response performance of the closed-loop system. Examples and simulations are presented to illustrate the analysis results. |
| format | Article |
| id | doaj-art-3b335458ecaf4981b3e088049efaf064 |
| institution | Kabale University |
| issn | 1687-5249 1687-5257 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Control Science and Engineering |
| spelling | doaj-art-3b335458ecaf4981b3e088049efaf0642025-02-03T01:26:09ZengWileyJournal of Control Science and Engineering1687-52491687-52572011-01-01201110.1155/2011/719730719730Stability and Performance of First-Order Linear Time-Delay Feedback Systems: An Eigenvalue ApproachShu-An He0I-Kong Fong1Department of Electrical Engineering, National Taiwan University, Taipei 10617, TaiwanDepartment of Electrical Engineering, National Taiwan University, Taipei 10617, TaiwanLinear time-delay systems with transcendental characteristic equations have infinitely many eigenvalues which are generally hard to compute completely. However, the spectrum of first-order linear time-delay systems can be analyzed with the Lambert function. This paper studies the stability and state feedback stabilization of first-order linear time-delay system in detail via the Lambert function. The main issues concerned are the rightmost eigenvalue locations, stability robustness with respect to delay time, and the response performance of the closed-loop system. Examples and simulations are presented to illustrate the analysis results.http://dx.doi.org/10.1155/2011/719730 |
| spellingShingle | Shu-An He I-Kong Fong Stability and Performance of First-Order Linear Time-Delay Feedback Systems: An Eigenvalue Approach Journal of Control Science and Engineering |
| title | Stability and Performance of First-Order Linear Time-Delay Feedback Systems: An Eigenvalue Approach |
| title_full | Stability and Performance of First-Order Linear Time-Delay Feedback Systems: An Eigenvalue Approach |
| title_fullStr | Stability and Performance of First-Order Linear Time-Delay Feedback Systems: An Eigenvalue Approach |
| title_full_unstemmed | Stability and Performance of First-Order Linear Time-Delay Feedback Systems: An Eigenvalue Approach |
| title_short | Stability and Performance of First-Order Linear Time-Delay Feedback Systems: An Eigenvalue Approach |
| title_sort | stability and performance of first order linear time delay feedback systems an eigenvalue approach |
| url | http://dx.doi.org/10.1155/2011/719730 |
| work_keys_str_mv | AT shuanhe stabilityandperformanceoffirstorderlineartimedelayfeedbacksystemsaneigenvalueapproach AT ikongfong stabilityandperformanceoffirstorderlineartimedelayfeedbacksystemsaneigenvalueapproach |