谢聂稳定判据

Xie-Nie's Stability Criterion

摘要: 谢绪恺、聂义勇判据的^1，2比国外学者的同类发现⁴要早得多．由于历史原因，这判据过去未曾宣扬．81年本刊上的简要介绍³曾引起了我国广大读者的重视和兴趣．现在，应读者要求，再作一次较详细的介绍．谢聂判据，简单地说，就是：（A）给多项式式a₀xⁿ+a₁x^n-1+…+a_n或a₀+a₁+…+a_nxⁿ（a_i>0，i=0，1，2，…n）定义一判定系数α_i=a_i-|a|+2/a_ia_i+1，（B）多项式所表征的系统的稳定性由这判定系数a_i判定，稳定的必要条件是a_i<1，充分条件是a_i<0.4655．

Abstract: Xie Xukai(Hsieh Hsük'ai) and Nie Yiyong (Nieh Yiyung) Criterion had been proposed much earlier than the similar ones in foreign countries.But it was unknown to the public owing to some historical reasons.A brief mention of that in this journal last year(Vol.10,No.1,1981) has aroused great interest and attention among readers in China.On their request,a more detailed exposition of the criterion is given