Quasi L₂/L₂ Hankel Norms and L₂/L₂ Hankel Norm/Operator of Sampled-Data Systems
抄録
This article is relevant to appropriately defining the L₂/L₂ Hankel norm of sampled-data systems through setting a general time instant Θ at which past and future are to be separated and introducing the associated quasi L₂/L₂ Hankel operator/norm at Θ . We first provide a method for computing the quasi L₂/L₂ Hankel norm for each Θ , which is carried out by introducing a shifted variant of the standard lifting technique for sampled-data systems. In particular, it is shown that the quasi L₂/L₂ Hankel norm can be represented as the l₂/l₂ Hankel norm of a Θ -dependent discrete-time system. It is further shown that an equivalent discretization of the generalized plant exists, which means that the aforementioned discrete-time system can be represented as the feedback connection of the discretized plant and the same discrete-time controller as the one in the sampled-data system. It is also shown that the supremum of the quasi L₂/L₂ Hankel norms at Θ belonging to a sampling interval is actually attained as the maximum, which means that what is called a critical instant always exists and the L₂/L₂ Hankel operator is always definable (as the quasi L₂/L₂ Hankel operator at the critical instant). Finally, we illustrate those theoretical developments through a numerical example.
収録刊行物
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- IEEE Transactions on Automatic Control
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IEEE Transactions on Automatic Control 68 (7), 4428-4434, 2023-07
Institute of Electrical and Electronics Engineers (IEEE)
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詳細情報 詳細情報について
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- CRID
- 1050298355878423808
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- ISSN
- 15582523
- 00189286
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- HANDLE
- 2433/286207
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- 本文言語コード
- en
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- 資料種別
- journal article
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- データソース種別
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- IRDB