| Title:
|
Notes on $\mu$ and $l_1$ robustness tests (English) |
| Author:
|
Kovács, Gábor Z. |
| Author:
|
Hangos, Katalin M. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
34 |
| Issue:
|
5 |
| Year:
|
1998 |
| Pages:
|
[565]-578 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An upper bound for the complex structured singular value related to a linear time-invariant system over all frequencies is given. It is in the form of the spectral radius of the ${\cal H}_\infty $-norm matrix of SISO input-output channels of the system when uncertainty blocks are SISO. In the case of MIMO uncertainty blocks the upper bound is the $\infty $-norm of a special non-negative matrix derived from ${\cal H}_\infty $-norms of SISO channels of the system. The upper bound is fit into the inequality relation between the results of $\mu $ and $\ell _1$ robustness tests. (English) |
| Keyword:
|
linear time-invariant MIMO system |
| Keyword:
|
robust stability |
| Keyword:
|
single input single output input-output channels |
| Keyword:
|
MIMO uncertainty |
| Keyword:
|
${\cal H}_\infty $-norm |
| MSC:
|
93B35 |
| MSC:
|
93C05 |
| MSC:
|
93C35 |
| MSC:
|
93D09 |
| idZBL:
|
Zbl 1274.93218 |
| idMR:
|
MR1663740 |
| . |
| Date available:
|
2009-09-24T19:20:36Z |
| Last updated:
|
2015-03-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135244 |
| . |
| Reference:
|
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| Reference:
|
[2] Dahleh M. A., Diaz–Bobillo I. J.: Control of Uncertain Systems.A Linear Programming Approach. Prentice Hall, NJ 1995 Zbl 0838.93007 |
| Reference:
|
[3] Doyle J. C.: Structured uncertainty in control system design.In: Proc. of 24th Conference on Decision and Control, Ft. Lauderdale FL 1985, pp. 260–265 |
| Reference:
|
[4] Fiedler M.: Special Matrices and Their Application in Numerical Mathematics.SNTL – Nakladatelství technické literatury, Prague 1981 Zbl 0531.65008 |
| Reference:
|
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| Reference:
|
[6] Khammash M. H., Pearson J. B.: Analysis and design for robust performance with structured uncertainty.Systems Control Lett. 20 (1993), 179–187 Zbl 0768.93065, MR 1208518, 10.1016/0167-6911(93)90059-F |
| Reference:
|
[7] Khammash M. H.: Necessary and sufficient conditions for the robustness of time–varying systems with applications to sampled–data systems.IEEE Trans. Automat. Control 38 (1993), 49–57 Zbl 0777.93018, MR 1201494, 10.1109/9.186311 |
| Reference:
|
[8] Packard A., Doyle J. C.: The complex structured singular value.Automatica 29 (1993), 71–109 Zbl 0772.93023, MR 1200542, 10.1016/0005-1098(93)90175-S |
| Reference:
|
[9] Tits A. L., Fan M. K. H.: On the small–$\mu $ theorem.Automatica 31 (1995), 1199–1201 Zbl 0831.93021, MR 1342128, 10.1016/0005-1098(95)00035-U |
| . |
