{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:46:35Z","timestamp":1760237195382,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,3,6]],"date-time":"2020-03-06T00:00:00Z","timestamp":1583452800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012639","name":"Prince Sultan University","doi-asserted-by":"publisher","award":["RG-DES-2017-01-17"],"award-info":[{"award-number":["RG-DES-2017-01-17"]}],"id":[{"id":"10.13039\/501100012639","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The numerical approximation of the    \u03bc   -value is key towards the measurement of instability, stability analysis, robustness, and the performance of linear feedback systems in system theory. The MATLAB function mussv available in MATLAB Control Toolbox efficiently computes both lower and upper bounds of the    \u03bc   -value. This article deals with the numerical approximations of the lower bounds of    \u03bc   -values by means of low-rank ordinary differential equation (ODE)-based techniques. The numerical simulation shows that approximated lower bounds of    \u03bc   -values are much tighter when compared to those obtained by the MATLAB function mussv.<\/jats:p>","DOI":"10.3390\/computation8010016","type":"journal-article","created":{"date-parts":[[2020,3,9]],"date-time":"2020-03-09T05:37:34Z","timestamp":1583732254000},"page":"16","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Instability Analysis of Linear Feedback Systems"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5828-3133","authenticated-orcid":false,"given":"Mutti-Ur","family":"Rehman","sequence":"first","affiliation":[{"name":"Department of Mathematics, Sukkur IBA University, Sukkur 65200, Pakistan"},{"name":"Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5262-1138","authenticated-orcid":false,"given":"Jehad","family":"Alzabut","sequence":"additional","affiliation":[{"name":"Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 12435, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1049\/ip-d.1982.0053","article-title":"Analysis of feedback systems with structured uncertainties","volume":"129","author":"Doyle","year":"1982","journal-title":"IEE Proc. 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