Robust Stability and Stable Member Problems for Multilinear Systems

Şerife Yılmaz

doi:10.17776/csj.1083550

EN

Robust Stability and Stable Member Problems for Multilinear Systems

Abstract

In this paper, we consider robust stability and stable member problems for linear systems whose characteristic polynomials are nonmonic polynomials with multilinear uncertainty. For both problems, the results are given by using the reflection (box) coefficients and the extreme point property of multilinear functions defined on the box. Finding stable member in a polynomial family is one of the hard problems of linear control theory. This issue is considered by visualizing the cases n-l=2 and n-l=3. Necessary and sufficient conditions for robust stability and the existence of a stable member of the multilinear polynomial family using the reflection coefficients are obtained. Several examples are provided.

Keywords

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Şerife Yılmaz ^*
0000-0002-7561-3288
Türkiye

Publication Date

September 30, 2022

Submission Date

March 6, 2022

Acceptance Date

August 5, 2022

Published in Issue

Year 2022 Volume: 43 Number: 3

DOI

https://doi.org/10.17776/csj.1083550

IZ

https://izlik.org/JA58YZ83MF

Cite

RIS / Bibtex

APA

Yılmaz, Ş. (2022). Robust Stability and Stable Member Problems for Multilinear Systems. Cumhuriyet Science Journal, 43(3), 492-496. https://doi.org/10.17776/csj.1083550

AMA

1.Yılmaz Ş. Robust Stability and Stable Member Problems for Multilinear Systems. CSJ. 2022;43(3):492-496. doi:10.17776/csj.1083550

Chicago

Yılmaz, Şerife. 2022. “Robust Stability and Stable Member Problems for Multilinear Systems”. Cumhuriyet Science Journal 43 (3): 492-96. https://doi.org/10.17776/csj.1083550.

EndNote

Yılmaz Ş (September 1, 2022) Robust Stability and Stable Member Problems for Multilinear Systems. Cumhuriyet Science Journal 43 3 492–496.

IEEE

[1]Ş. Yılmaz, “Robust Stability and Stable Member Problems for Multilinear Systems”, CSJ, vol. 43, no. 3, pp. 492–496, Sept. 2022, doi: 10.17776/csj.1083550.

ISNAD

Yılmaz, Şerife. “Robust Stability and Stable Member Problems for Multilinear Systems”. Cumhuriyet Science Journal 43/3 (September 1, 2022): 492-496. https://doi.org/10.17776/csj.1083550.

JAMA

1.Yılmaz Ş. Robust Stability and Stable Member Problems for Multilinear Systems. CSJ. 2022;43:492–496.

MLA

Yılmaz, Şerife. “Robust Stability and Stable Member Problems for Multilinear Systems”. Cumhuriyet Science Journal, vol. 43, no. 3, Sept. 2022, pp. 492-6, doi:10.17776/csj.1083550.

Vancouver

1.Şerife Yılmaz. Robust Stability and Stable Member Problems for Multilinear Systems. CSJ. 2022 Sep. 1;43(3):492-6. doi:10.17776/csj.1083550