Abstract
In the paper a method of studying forms of odd degree in some cone of a domain of the space\(R^{\underline n } \) is given,which allows us to use as functions the Lyapunov forms of arbitrarily high degree. It is shown that anapplication of such forms gives a possibility of obtaining conditions on monotonic stability of one modelsystem with a polynomial right-hand side of a special form. With the help of forms of high degree we modifythe known theorem on an exponential stability, and also the possibility of using them as components of avector Lyapunov function in the study of stability of complex systems is shown.
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Translated from Dinamicheskie Sistemy, No. 7, pp. 89–95, 1988.
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Persidskii, S.K., Stepanov, A.V. On an application of forms of arbitrarily high degree as the Lyapunov functions. J Math Sci 65, 1559–1563 (1993). https://doi.org/10.1007/BF01097664
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DOI: https://doi.org/10.1007/BF01097664