# Article

 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: [1] Dahleh M. A., Khammash M.: Controller design for plants with structured uncertainty.Automatica 29 (1993), 37–56 Zbl 0772.93028, MR 1200540, 10.1016/0005-1098(93)90173-Q 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: [5] Khammash M. H., Pearson J. B.: Performance robustness of discrete–time systems with structured uncertainty.IEEE Trans. Automat. Control 36 (1991), 398–412 Zbl 0754.93063, MR 1097093, 10.1109/9.75099 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 .

## Files

Files Size Format View
Kybernetika_34-1998-5_6.pdf 1.945Mb application/pdf View/Open

Partner of