特征方程的常数项的稳定区确定法
An Approach to Determine the Stable Interval of the Constant Term of a Characteristic Equation
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摘要: 应用多项式的增广图示知识,可以得到确定特征方程常数项an的稳定区的准则.由于an本身不参加计算,而且得到的是an稳定区,不只是一组系数的判别,所以这个判别线性系统稳定性的方法具有一定的优点.对于特征方程次数n≤10都能用公式计算.当n=5或6时判别尤为便捷若n≥11.不得不依靠解数字方程才行.Abstract: In this paper, an approach is introduced to determine the stable interval of the constant term of a characteristic equation by using the theory of extended graphical representation of polynomials. Because the constant an itself is not taken into account and because this method is to get a stable interval of an, not merely to make a stability test for a set of known coefficients, this method of stability criteria has some advantages over the others. The interval of an can be obtained from the calculation of some algebraical expressions when n≤10 where n is the degree of the characteristic equation. It is very convenient to calculate for the cases n=5 and n=6. When n≥11, this interval can be found only by the method of numerical solutions.
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