International journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN:2313-626X

Frequency: 12
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 Volume 5, Issue 12 (December 2018), Pages: 119-125

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 Original Research Paper

 Title: Approximating structured singular values for discrete Fourier transformation matrices

 Author(s): Mutti-Ur Rehman 1, *, Arshad Mehmood 2

 Affiliation(s):

 1Department of Mathematics, Sukkur IBA University, 65200 Sukkur, Pakistan
 2Department of Mathematics, University of Lahore, Gujrat campus, 50700 Gujrat, Pakistan

 https://doi.org/10.21833/ijaas.2018.12.014

 Full Text - PDF          XML

 Abstract:

In this article, we present the numerical computations of singular values and lower bounds of structured singular values, known as μ-values, for a family of Discrete Fourier Transform matrices. The μ-value is a well-known mathematical tool in linear control theory which speaks about the stability and instability analysis of feedback systems. The comparison of lower bounds of μ-values with the well-known MATLAB routine mussv is investigated. 

 © 2018 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Singular values, Structured singular values, Spectral radius, Low rank ODE’s, Gradient system of ODE’s

 Article History: Received 12 July 2018, Received in revised form 11 October 2018, Accepted 17 October 2018

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2018.12.014

 Citation:

 Rehman M and Mehmood A (2018). Approximating structured singular values for discrete Fourier transformation matrices. International Journal of Advanced and Applied Sciences, 5(12): 119-125

 Permanent Link:

 http://www.science-gate.com/IJAAS/2018/V5I12/Rehman.html

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 References (10) 

  1. Braatz RP, Young PM, Doyle JC, and Morari M (1994). Computational complexity of/spl mu/calculation. IEEE Transactions on Automatic Control, 39(5): 1000-1002. https://doi.org/10.1109/9.284879  [Google Scholar]
  1. Chen J, Fan MK, and Nett CN (1996). Structured singular values with nondiagonal structures. I. Characterizations. IEEE Transactions on Automatic Control, 41(10): 1507-1511. https://doi.org/10.1109/9.539434   [Google Scholar]
  1. Fan MK, Tits AL, and Doyle JC (1991). Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics. IEEE Transactions on Automatic Control, 36(1): 25-38. https://doi.org/10.1109/9.62265  [Google Scholar]
  1. Hinrichsen D and Pritchard AJ (2005). Mathematical systems theory I: modelling, state space analysis, stability and robustness. Vol. 48, Springer, Berlin, Germany. https://doi.org/10.1007/b137541  [Google Scholar]
  1. Karow M, Kokiopoulou E, and Kressner D (2010). On the computation of structured singular values and pseudospectra. Systems and Control Letters, 59(2): 122-129. https://doi.org/10.1016/j.sysconle.2009.12.007  [Google Scholar]
  1. Karow M, Kressner D, and Tisseur F (2006). Structured eigenvalue condition numbers. SIAM Journal on Matrix Analysis and Applications, 28(4): 1052-1068. https://doi.org/10.1137/050628519  [Google Scholar]
  1. Packard A and Doyle J (1993). The complex structured singular value. Automatica, 29(1): 71-109. https://doi.org/10.1016/0005-1098(93)90175-S  [Google Scholar]
  1. Packard A, Fan MK, and Doyle J (1988). A power method for the structured singular value. In the 27th IEEE Conference on Decision and Control, IEEE, Austin, USA: 2132-2137.  [Google Scholar]
  1. Qiu L, Bernhardsson B, Rantzer A, Davison EJ, Young PM, and Doyle JC (1995). A formula for computation of the real stability radius. Automatica, 31(6): 879-890. https://doi.org/10.1016/0005-1098(95)00024-Q  [Google Scholar]
  1. Rehman MU (2017). Structured singular values for Bernoulli matrices. International Journal of Advances in Applied Mathematics and Mechanics, 4(4): 41-49.  [Google Scholar]