拓广的盒子定理

THE EXTENDED BOX THEOREM

本文给出了当线性系统的传递函数为区间有理函数时的系统闭环鲁棒稳定性及多项式族δ~1(s)=sum from i=0 to m(Q_i(s)P_i(s))的鲁棒稳定的充要条件。Q_i(s)满足某些假定条件后,得出了δ(s)鲁棒稳定性的有限检验的充要条件。

This paper shows the robust stablility of closed-loop systems with rational tranfer function, and gives a necessary and sufficient condition for robust stability of polynomial family δ(s) =Q_o(s)P_o(s)+…+Q_m(s)P_m(s). It states a necessary and sufficient finite checking for robust stability of polynomial family δ(s) when Q_i(s) satisfies some assumptions, and when Q_i(s) is a general polynomial,a so-called edge-checking for robust stability of δ(s) is obtained.