{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:09:39Z","timestamp":1760238579402,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,8,29]],"date-time":"2020-08-29T00:00:00Z","timestamp":1598659200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article we present an ordinary differential equation based technique to study the quadratic stability of non-linear dynamical systems. The non-linear dynamical systems are modeled with norm bounded linear differential inclusions. The proposed methodology reformulate non-linear differential inclusion to an equivalent non-linear system. Lyapunov function demonstrate the existence of a symmetric positive definite matrix to analyze the stability of non-linear dynamical systems. The proposed method allows us to construct a system of ordinary differential equations to localize the spectrum of perturbed system which guarantees the stability of non-linear dynamical system.<\/jats:p>","DOI":"10.3390\/sym12091432","type":"journal-article","created":{"date-parts":[[2020,8,30]],"date-time":"2020-08-30T06:06:22Z","timestamp":1598767582000},"page":"1432","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Quadratic Stability of Non-Linear Systems Modeled with Norm Bounded Linear Differential Inclusions"],"prefix":"10.3390","volume":"12","author":[{"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 11586, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arfan","family":"Hyder","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sukkur IBA University, Sukkur 65200, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1109\/9.481616","article-title":"Necessary and sufficient conditions for quadratic stability and stabilizability of uncertain linear time-varying systems","volume":"41","author":"Amato","year":"1996","journal-title":"IEEE Trans. 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