多项式稳定的新几何判据

A new geometric criterion for polynomial stability

研究了多项式f_n(z)的稳定性及稳定度的判定,首先利用实系数多项式f_n(z)零点的共轭性和界限性,给出了基于角度的简单加减计算的新几何判据,其理论更为简捷,证明方法更为直观、初等.且通过计算程序化易于绘制近似特征曲线,从而能够更加方便地进行判定.其次,进一步应用数值实例来验证新几何判据的可行性及优越性.

This paper studies the stability of polynomial f n（z） and its judgment. Firstly, using the conjugacy and boundaries of zeros of real coefficient polynomial, it gives a new geometric criterion for a simple addition and subtraction based on arc angle, its theory is simpler and its proof is easier and more intuitive. What s more, it is easy to draw an approximate characteristic curve by programming computation, and thus it can more easily make decisions. Then,the numerical example is given to show the potential and validity of the new geometric criterion.