Acta Scientiarum Naturalium Universitatis Pekinensis

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Some Geometrical Properties of Stable Matrix Families

YU Xuegang, HUANG Lin   

  1. Dept. of Mechanics & Engineering Science, Peking University, Beijing, 100871
  • Received:1998-06-24 Online:1999-09-20 Published:1999-09-20



  1. 北京大学力学与工程科学系,北京,100871

Abstract: In this paper, we have discussed the convex directions of Hurwitz and Schur matices, then the necessary and sufficient conditions are obtained. Using these results, the continuous connection of two D-matices problem is considered, when the D set is convex, it is shown that the set which is consisted of D-matrices is connected. Then we also discuss the analogical questions in the case of polynomials.

Key words: convex direction, Hurwitz stability, Schur stability

摘要: 讨论了 Hurwitz 和 Schur矩阵的凸方向问题,并给出了其充要条件。利用有关结果,给出了两个D-稳定矩阵之间连续过渡的问题,结果表明,只要D为一凸集,则所有D-稳定矩阵构成的集合是连通的。进而讨论了多项式情况下类似的问题。

关键词: 凸方向, Hurwitz稳定性, Schur稳定性

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