系数空间中多项式的鲁棒稳定性和有理函数的严格正实不变性*

Robust Stability of Polynomials and Strictly Positive Realness Invariance of Rational Functions in Coefficient Space

中文关键词  线性系统  多项式  有理函数  稳定性  鲁棒性  严格正实  系数空间

英文关键词  linear systems  polynomials  rational functions  stability  robustness  strict positive realness  coefficient space

中文摘要

      本文在多项式的系数空间中讨论离散时间意义下多项式的鲁棒稳定性和有理函数的严格正实不变性，证明了对于系数空间中的某种超矩形，其顶点多项式的稳定性就保证了全族无穷个多项式的稳定性；对于有理函数的严格正实性，本文也得到了类似的结论。

英文摘要

      This paper discusses robust stability of polynomials and strictly positive realness invariance of rational functions in coefficient space in the sense of discrete time. We prove that, for certain superrectangle in coefficient space, the stability of all vertex polynomials implies the stability of the whole family. Similar results have been obtained for the strict positive realness of rational functions.