复系数区间多项式Kharitonov定理的一个新证明

A New Proof to Kharitonov's Theorem of Interval Polynomials with Complex Coefficients

Kharitonov定理在复系数区间多项式下扩展形式指出,实部和虚部均在特定区间内任意取值的复系数区间多项式族是Hurwitz稳定的,当且仅当8个特定顶点多项式是Hurwitz稳定的。本文未采用复杂的Hermite-Biehler定理,基于著名的排零原理,对上述结果给出了一个新的简单的证明。

Kharitonov's theorem generalized to polynomials with complex coefficients reveals that the family of interval polynomials,in which real and imaginary parts of each coefficient vary in a given interval,are Hurwitz if and only if eight special,well-defined polynomials are Hurwitz.This paper gives a new simple proof of the theorem by using the classical zero exclusion principle without invoking the Hermite-Biehler theorem.