Abstract
A new approach to validation of a number of algebraic stability criteria and theorems on localization of the roots of a complex polynomial in the complex plane is proposed. The solution is based on theorems relating complex polynomials and methods for the synthesis of reactive and quasi-reactive one-port networks. Analogs of the Routh tabular criterion and the Hermite–Hurwitz determinant criterion are considered, including critical cases. It is shown that the Routh algorithm is unsurpassed in simplicity and accuracy of calculations. Application of the criteria is illustrated by the analysis of the models of real dynamic systems, namely, two- and three-circuit oscillators with close eigenfrequencies.
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