{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:57:50Z","timestamp":1754157470345,"version":"3.41.2"},"reference-count":17,"publisher":"Emerald","issue":"3\/4","license":[{"start":{"date-parts":[[2009,4,10]],"date-time":"2009-04-10T00:00:00Z","timestamp":1239321600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,4,10]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to discuss the Schur D\u2010stability and the vertex stability of interval matrices (including point matrix obviously). Some new sufficient conditions (criteria) are proposed which guarantee the interval matrix is Schur D\u2010stable. This results are shown to be less conservative than those in recent literatures. In addition, two equivalence relations between the Schur D\u2010stability and the vertex stability of interval matrices will be proposed and a new Schur D\u2010stability range of an interval matrix presented.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>Matrix eigenvalues theory and matrix measure approach.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>Several simple sufficient conditions (criteria) for guaranteeing the Schur D\u2010stability of interval matrices are derived, two equivalence relations between the Schur D\u2010stability and the vertex stability of interval matrices are proposed, and a new Schur D\u2010stability range of an interval matrix is presented.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Research limitations\/implications<\/jats:title><jats:p>Control theory or stability theory. These stability criterion possess simple forms and provide useful tools to check Schur D\u2010stability of interval matrices (including point matrix) at first stage.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>The paper provides useful tools to check Schur D\u2010stability of interval matrices (including point matrix) at first stage.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>Two equivalence relations between the Schur D\u2010stability and the vertex stability for general interval matrices (including point matrix) are proposed, such that the conditional limitations for tridiagonal matrix in recent papers are broken. A new Schur D\u2010stability range of an interval matrix is presented, and several simple sufficient conditions are obtained which guarantee the Schur D\u2010stability of interval matrices (including point matrix).<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910944182","type":"journal-article","created":{"date-parts":[[2009,5,30]],"date-time":"2009-05-30T07:05:39Z","timestamp":1243667139000},"page":"474-480","source":"Crossref","is-referenced-by-count":1,"title":["New sufficient criteria for Schur D\u2010stability of interval matrices"],"prefix":"10.1108","volume":"38","author":[{"given":"Gui\u2010Ju","family":"Shi","sequence":"first","affiliation":[]},{"given":"Jin\u2010Fang","family":"Han","sequence":"additional","affiliation":[]},{"given":"Jun\u2010Ling","family":"Gao","sequence":"additional","affiliation":[]},{"given":"Qing\u2010Yin","family":"Wang","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022020919575544000_b3","doi-asserted-by":"crossref","unstructured":"Berman, A. 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