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Abstract <p>A matrix polynomial is said to be stable or antistable, according as all its eigenvalues lie in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7215_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(|z|&lt;1\)</EquationSource> <!--ContMath2360107Monga-m1--> </InlineEquation> or <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7215_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="57" /> </InlineMediaObject> <EquationSource Format="TEX">\(|z|\geq 1,\)</EquationSource> <!--ContMath2360107Monga-m2--> </InlineEquation> respectively. In this paper, among other things, we prove some necessary conditions for a matrix polynomial to be stable or antistable. Furthermore, we obtain a sufficient condition for a matrix polynomial to be stable.</p>

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Some Results on the Stability of Matrix Polynomials

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Z. B. Monga,
  • W. M. Shah

摘要

Abstract

A matrix polynomial is said to be stable or antistable, according as all its eigenvalues lie in \(|z|<1\) or \(|z|\geq 1,\) respectively. In this paper, among other things, we prove some necessary conditions for a matrix polynomial to be stable or antistable. Furthermore, we obtain a sufficient condition for a matrix polynomial to be stable.