| Title:
|
On approximation of stability radius for an infinite-dimensional feedback control system (English) |
| Author:
|
Sano, Hideki |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
52 |
| Issue:
|
5 |
| Year:
|
2016 |
| Pages:
|
824-835 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we discuss the problem of approximating stability radius appearing in the design procedure of finite-dimensional stabilizing controllers for an infinite-dimensional dynamical system. The calculation of stability radius needs the value of $H_\infty$-norm of a transfer function whose realization is described by infinite-dimensional operators in a Hilbert space. From the computational point of view, we need to prepare a family of approximate finite-dimensional operators and then to calculate the $H_\infty$-norm of their transfer functions. However, it is not assured that they converge to the value of $H_\infty$-norm of the original transfer function. The purpose of this study is to justify the convergence. In a numerical example, we treat parabolic distributed parameter systems with distributed control and distributed/boundary observation. (English) |
| Keyword:
|
distributed parameter system |
| Keyword:
|
finite-dimensional controller |
| Keyword:
|
stability radius |
| Keyword:
|
transfer function |
| Keyword:
|
semigroup |
| MSC:
|
93C25 |
| MSC:
|
93D15 |
| idZBL:
|
Zbl 06674941 |
| idMR:
|
MR3602017 |
| DOI:
|
10.14736/kyb-2016-5-0824 |
| . |
| Date available:
|
2017-01-02T13:33:24Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145970 |
| . |
| Reference:
|
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| Reference:
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