线性离散系统的一个简化稳定性判据

E. Jury
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引用次数: 108

摘要

本文给出了线性离散系统稳定性的一种简化解析检验方法。这个检验也得到了变量z的实多项式的所有根都在z平面的单位圆内的充分必要条件。新的稳定性约束只需要计算一半的Schur-Cohn行列式[1],[2]。证明了对于四阶系统的检验只需要一个三阶行列式,而对于五阶系统的检验则需要一个二阶行列式和一个四阶行列式。该测试直接应用于z平面,并产生最小数量的约束项。得到了六阶情况下的稳定性约束,并给出了n阶情况下的稳定性约束公式。该准则的简单性与连续情况下的Lienard-Chipard准则[3]相似,与roth - hurwitz准则[4],[5]相比具有决定性的优势。最后,给出了单位圆内n个偶数和奇数根个数的一般条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Simplified Stability Criterion for Linear Discrete Systems
In this study a simplified analytic test of stability of linear discrete systems is obtained. This test also yields the necessary and sufficient conditions for a real polynomial in the variable z to have all its roots inside the unit circle in the z plane. The new stability constraints require the evaluation of only half the number of Schur-Cohn determinants [1], [2]. It is shown that for the test of a fourth-order system only a third-order determinant is required and for the fifth-order, one second-order and one fourth-order determinant are required. The test is applied directly in the z plane and yields the minimum number of constraint terms. Stability constraints up to the sixth-order case are obtained and for the nth-order case are formulated. The simplicity of this criterion is similar to that of the Lienard-Chipard criterion [3] for the continuous case which has a decisive advantage over the Routh-Hurwitz criterion [4], [5]. Finally, general conditions on the number of roots inside the unit circle for n even and odd are also presented in this paper.
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