Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems

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Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems. / Leonov, G. A.; Kuznetsov, N. V.

In: Doklady Mathematics, Vol. 84, No. 1, 08.2011, p. 475-481.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{eb3a9c5b814f484a9544db8ed3476554,

title = "Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems",

abstract = "Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems are developed. This includes the harmonic balance method and the construction of counterexamples to Kalman's problem. An analytical criterion for the existence of periodic solutions is proved, such that the existence of hidden oscillations, a basin of attraction of which does not contain neighborhoods of equilibria, is detected. To construct a counterexample to Kalman's problem, the computational procedure is developed for the sequence of nonlinearities. The recursive construction of periodic solutions is found by replacing the nonlinearity by the strictly increasing function. The successive construction of periodic solutions for system is found by replacing the nonlinearity by the strictly increasing function.",

author = "Leonov, {G. A.} and Kuznetsov, {N. V.}",

note = "Funding Information: ACKNOWLEDGMENTS This work was supported by the Ministry of Educa tion and Science of Russian Federation, St. Petersburg State University, and the Academy of Finland.",

year = "2011",

month = aug,

doi = "10.1134/S1064562411040120",

language = "English",

volume = "84",

pages = "475--481",

journal = "Doklady Mathematics",

issn = "1064-5624",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "1",

}

RIS

TY - JOUR

T1 - Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems

AU - Leonov, G. A.

AU - Kuznetsov, N. V.

N1 - Funding Information: ACKNOWLEDGMENTS This work was supported by the Ministry of Educa tion and Science of Russian Federation, St. Petersburg State University, and the Academy of Finland.

PY - 2011/8

Y1 - 2011/8

N2 - Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems are developed. This includes the harmonic balance method and the construction of counterexamples to Kalman's problem. An analytical criterion for the existence of periodic solutions is proved, such that the existence of hidden oscillations, a basin of attraction of which does not contain neighborhoods of equilibria, is detected. To construct a counterexample to Kalman's problem, the computational procedure is developed for the sequence of nonlinearities. The recursive construction of periodic solutions is found by replacing the nonlinearity by the strictly increasing function. The successive construction of periodic solutions for system is found by replacing the nonlinearity by the strictly increasing function.

AB - Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems are developed. This includes the harmonic balance method and the construction of counterexamples to Kalman's problem. An analytical criterion for the existence of periodic solutions is proved, such that the existence of hidden oscillations, a basin of attraction of which does not contain neighborhoods of equilibria, is detected. To construct a counterexample to Kalman's problem, the computational procedure is developed for the sequence of nonlinearities. The recursive construction of periodic solutions is found by replacing the nonlinearity by the strictly increasing function. The successive construction of periodic solutions for system is found by replacing the nonlinearity by the strictly increasing function.

UR - http://www.scopus.com/inward/record.url?scp=80053141035&partnerID=8YFLogxK

U2 - 10.1134/S1064562411040120

DO - 10.1134/S1064562411040120

M3 - Article

VL - 84

SP - 475

EP - 481

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 1

ER -

ID: 5366616