Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T05:23:41.098Z Has data issue: false hasContentIssue false
  • English
  • Français

STRUCTURED SINGULAR VALUES OF SOME GENERALISED STOCHASTIC MATRICES

Part of: Special matrices Basic linear algebra

Published online by Cambridge University Press:  09 July 2021

KIJTI RODTES Open the ORCID record for KIJTI RODTES [Opens in a new window]  and
MUTTI UR REHMAN ABBASI Open the ORCID record for MUTTI UR REHMAN ABBASI [Opens in a new window]
KIJTI RODTES*
Affiliation:
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
MUTTI UR REHMAN ABBASI
Affiliation:
Department of Mathematics, Sukkur IBA University, 65200 Sukkur, Pakistan and Department of Chemical Engineering, MIT, Cambridge, MA 02139, USA e-mail: mutti.rehman@iba-suk.edu.pk, muttiur@mit.edu
*
e-mail: kijtir@nu.ac.th
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate a class of generalised stochastic complex matrices constructed from the class of all doubly stochastic matrices and a special class of circulant matrices. We determine the exact values of the structured singular values of all matrices in the class in terms of the constant row (column) sum.

Keywords

structured singular valuegeneralised doubly stochastic matrixnorm of a matrix

MSC classification

Primary: 15A18: Eigenvalues, singular values, and eigenvectors
Secondary: 15B51: Stochastic matrices 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 1 , February 2022 , pp. 58 - 67
Check for updates
Copyright
© 2021 Australian Mathematical Publishing Association Inc.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Dahleh, M., Dahleh, M. A. and Verghese, G., Lectures on Dynamic Systems and Control (MIT OpenCourseWare, Cambridge, MA, 2003).Google Scholar
Doyle, J. C., ‘Analysis of feedback systems with structured uncertainties’, IEE Proc. D 129(6) (1982), 242–250.CrossRefGoogle Scholar
Doyle, J. C., Wall, J. and Stein, G., ‘Performance and robustness analysis for structured uncertainty’, Proc. 21st IEEE Conf. Decision Control (IEEE, Piscataway, NJ, 1982), 629–636.Google Scholar
Guglielmi, N., Rehman, M.-Ur and Kressner, D., ‘A novel iterative method to approximate structured singular values’, SIAM J. Matrix Anal. Appl. 38(2) (2017), 361–386.CrossRefGoogle Scholar
Packard, A. and Doyle, J. C., ‘Structured singular value with repeated scalar blocks’, Proc. 1988 American Control Conf. (IEEE, Piscataway, NJ, 1988), 1213–1218.CrossRefGoogle Scholar
Yamamoto, S. and Kimura, H., ‘On structured singular values of reciprocal matrices’, Proc. 1995 American Control Conf. (IEEE, Piscataway, NJ, 1995), 3358–3359.Google Scholar