On well‐definability of the L∞/L2 Hankel operator and detection of all the critical instants in sampled‐data systems
Abstract Because sampled‐data systems have h‐periodic nature with the sampling period h, an arbitrary Θ∈[0,h) is taken and the quasi L∞/L2 Hankel operator at Θ is defined as the mapping from L2(−∞,Θ) to L∞[Θ,∞). Its norm called the quasi L∞/L2 Hankel norm at Θ is used to define the L∞/L2 Hankel norm...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-03-01
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| Series: | IET Control Theory & Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1049/cth2.12069 |
| _version_ | 1818017732405231616 |
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| author | Tomomichi Hagiwara Akira Inai Jung Hoon Kim |
| author_facet | Tomomichi Hagiwara Akira Inai Jung Hoon Kim |
| author_sort | Tomomichi Hagiwara |
| collection | DOAJ |
| description | Abstract Because sampled‐data systems have h‐periodic nature with the sampling period h, an arbitrary Θ∈[0,h) is taken and the quasi L∞/L2 Hankel operator at Θ is defined as the mapping from L2(−∞,Θ) to L∞[Θ,∞). Its norm called the quasi L∞/L2 Hankel norm at Θ is used to define the L∞/L2 Hankel norm as the supremum of their values over Θ∈[0,h). If the supremum is actually attained as the maximum, then a maximum‐attaining Θ is called a critical instant and the L∞/L2 Hankel operator is said to be well‐definable. An earlier study establishes a computation method of the L∞/L2 Hankel norm, which is called a sophisticated method if our interest lies only in its computation. However, the feature of the method that it is free from considering the quasi L∞/L2 Hankel norm for any Θ∈[0,h) prevents the earlier study to give any arguments as to whether the obtained L∞/L2 Hankel norm is actually attained as the maximum, as well as detecting all the critical instants when the L∞/L2 Hankel operator is well‐definable. This paper establishes further arguments to tackle these relevant questions and provides numerical examples to validate the arguments in different aspects of authors' theoretical interests. |
| first_indexed | 2024-04-14T07:31:36Z |
| format | Article |
| id | doaj.art-ff072f23d0d44c8186a3703a6ce73909 |
| institution | Directory Open Access Journal |
| issn | 1751-8644 1751-8652 |
| language | English |
| last_indexed | 2024-04-14T07:31:36Z |
| publishDate | 2021-03-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Control Theory & Applications |
| spelling | doaj.art-ff072f23d0d44c8186a3703a6ce739092022-12-22T02:05:52ZengWileyIET Control Theory & Applications1751-86441751-86522021-03-0115566868210.1049/cth2.12069On well‐definability of the L∞/L2 Hankel operator and detection of all the critical instants in sampled‐data systemsTomomichi Hagiwara0Akira Inai1Jung Hoon Kim2Department of Electrical Engineering Kyoto University Kyoto JapanDepartment of Electrical Engineering Kyoto University Kyoto JapanDepartment of Electrical Engineering Pohang University of Science and Technology (POSTECH) Pohang Republic of KoreaAbstract Because sampled‐data systems have h‐periodic nature with the sampling period h, an arbitrary Θ∈[0,h) is taken and the quasi L∞/L2 Hankel operator at Θ is defined as the mapping from L2(−∞,Θ) to L∞[Θ,∞). Its norm called the quasi L∞/L2 Hankel norm at Θ is used to define the L∞/L2 Hankel norm as the supremum of their values over Θ∈[0,h). If the supremum is actually attained as the maximum, then a maximum‐attaining Θ is called a critical instant and the L∞/L2 Hankel operator is said to be well‐definable. An earlier study establishes a computation method of the L∞/L2 Hankel norm, which is called a sophisticated method if our interest lies only in its computation. However, the feature of the method that it is free from considering the quasi L∞/L2 Hankel norm for any Θ∈[0,h) prevents the earlier study to give any arguments as to whether the obtained L∞/L2 Hankel norm is actually attained as the maximum, as well as detecting all the critical instants when the L∞/L2 Hankel operator is well‐definable. This paper establishes further arguments to tackle these relevant questions and provides numerical examples to validate the arguments in different aspects of authors' theoretical interests.https://doi.org/10.1049/cth2.12069Combinatorial mathematicsDiscrete control systems |
| spellingShingle | Tomomichi Hagiwara Akira Inai Jung Hoon Kim On well‐definability of the L∞/L2 Hankel operator and detection of all the critical instants in sampled‐data systems IET Control Theory & Applications Combinatorial mathematics Discrete control systems |
| title | On well‐definability of the L∞/L2 Hankel operator and detection of all the critical instants in sampled‐data systems |
| title_full | On well‐definability of the L∞/L2 Hankel operator and detection of all the critical instants in sampled‐data systems |
| title_fullStr | On well‐definability of the L∞/L2 Hankel operator and detection of all the critical instants in sampled‐data systems |
| title_full_unstemmed | On well‐definability of the L∞/L2 Hankel operator and detection of all the critical instants in sampled‐data systems |
| title_short | On well‐definability of the L∞/L2 Hankel operator and detection of all the critical instants in sampled‐data systems |
| title_sort | on well definability of the l∞ l2 hankel operator and detection of all the critical instants in sampled data systems |
| topic | Combinatorial mathematics Discrete control systems |
| url | https://doi.org/10.1049/cth2.12069 |
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