Volume 7, Issue 8 (August 2020), Pages: 125-129

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 Original Research Paper

 Title: An analytical approach to compute lower bounds of 𝝁-values

 Author(s): Mutti-Ur Rehman ¹, Jehad Alzabut ^2, *, Sidrah Ahmed ¹

 Affiliation(s):

 ¹Department of Mathematics, Sukkur IBA University, Sukkur, Pakistan
 ²Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-5262-1138

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2020.08.013

 Abstract:

The lower bounds of values for a family of square real and complex valued matrices are computed analytically. The proposed methodology consists of factorizing an admissible perturbation from a set of block diagonal matrices into a block diagonal matrix. The computation of the lower bounds of values is then carried out by computing the spectral radius and numerical radius for matrix under consideration. The lower bounds of value provide the conditions which guarantee the instability analysis of the linear feedback system. 

 © 2020 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: Eigenvalues, Singular values, Structured singular values, Low rank ODEs

 Article History: Received 17 January 2020, Received in revised form 5 May 2020, Accepted 7 May 2020

 Acknowledgment:

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The authors declare that they have no conflict of interest.

 Citation:

 Rehman MU, Alzabut J, and Ahmed S (2020). An analytical approach to compute lower bounds of 𝝁-values. International Journal of Advanced and Applied Sciences, 7(8): 125-129

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