Abstract
We obtain a new criterion in terms of determinant inequalities that all the roots of a real polynomial should lie inside the unit circle, i.e., a criterion for the stability of periodic motions. In comparison with the Shur-Kon criterion, the number of determinants is halved.
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The results of this paper were published without proof in [2].
Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 3–12, January, 1973.
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Korsakov, G.F. The number of roots of a polynomial outside a circle. Mathematical Notes of the Academy of Sciences of the USSR 13, 3–8 (1973). https://doi.org/10.1007/BF01093620
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DOI: https://doi.org/10.1007/BF01093620