| Autor: |
Oe Ryung Kang, Jung Hoon Kim |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
AIMS Mathematics, Vol 8, Iss 12, Pp 29140-29157 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20231492?viewType=HTML |
| Popis: |
This paper develops a method for computing the $ l_{\infty} $-induced norm of a multivariable discrete-time linear system, for which an infinite-dimensional matrix should be intrinsically concerned with. To make such a computation feasible, we treat the infinite-dimensional matrix in a truncated fashion, and an upper bound and a lower bound on the $ l_\infty $-induced norm of the original multivariable discrete-time linear system are derived. More precisely, the matrix $ \infty $-norm of the (infinite-dimensional) tail part can be approximately computed by deriving its upper and lower bounds, while that of the (finite-dimensional) truncated part can be exactly obtained. With these values, an upper bound and a lower bound on the original $ l_\infty $-induced norm can be computed. Furthermore, these bounds are shown to converge to each other within an exponential order of $ N $, where $ N $ is the corresponding truncation parameter. Finally, some numerical examples are provided to demonstrate the theoretical validity and practical effectiveness of the developed computation method. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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