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On well‐definability of the L ∞ / L 2 Hankel operator and detection of all the critical instants in sampled‐data systems

Title
On well‐definability of the L ∞ / L 2 Hankel operator and detection of all the critical instants in sampled‐data systems
Authors
Hagiwara, TomomichiAkira, InaiKIM, JUNG HOON
Date Issued
Feb-2021
Publisher
Institution of Engineering and Technology
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.
URI
http://oasis.postech.ac.kr/handle/2014.oak/104720
ISSN
1751-8644
Article Type
Article
Citation
IET Control Theory and Applications, 2021-02
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