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About the necessity of Popov criterion for a special Lyapunov function existence for the systems with multiple nonlinearities. / Lipkovich, M.M.; Fradkov, A.L.

In: Automation and Remote Control, Vol. 76, No. 5, 2015, p. 801-808.

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

Harvard

Lipkovich, MM & Fradkov, AL 2015, 'About the necessity of Popov criterion for a special Lyapunov function existence for the systems with multiple nonlinearities', Automation and Remote Control, vol. 76, no. 5, pp. 801-808. https://doi.org/10.1134/S0005117915050069

APA

Lipkovich, M. M., & Fradkov, A. L. (2015). About the necessity of Popov criterion for a special Lyapunov function existence for the systems with multiple nonlinearities. Automation and Remote Control, 76(5), 801-808. https://doi.org/10.1134/S0005117915050069

Vancouver

Lipkovich MM, Fradkov AL. About the necessity of Popov criterion for a special Lyapunov function existence for the systems with multiple nonlinearities. Automation and Remote Control. 2015;76(5):801-808. https://doi.org/10.1134/S0005117915050069

Author

Lipkovich, M.M. ; Fradkov, A.L. / About the necessity of Popov criterion for a special Lyapunov function existence for the systems with multiple nonlinearities. In: Automation and Remote Control. 2015 ; Vol. 76, No. 5. pp. 801-808.

BibTeX

@article{f10559a6077b4c3696d89669fdd2dd42,
title = "About the necessity of Popov criterion for a special Lyapunov function existence for the systems with multiple nonlinearities",
abstract = "{\textcopyright} 2015, Pleiades Publishing, Ltd. Necessary and sufficient conditions for existence of Lyapunov function from the class “quadratic form plus integral of nonlinearity” (Lyapunov-Lurie function) for systems with several nonlinearities are considered. It is assumed that the nonlinearity graphs belong to the infinite sectors, i.e., belong to the union of the first and third quadrants in the plane. It is proven that Popov criterion is necessary and sufficient for existence of Lyapunov-Lurie function if the relative degree of the linear part is greater than one. The proof is based on the result concerning losslessness of the S-procedure for several respective quadratic constraints.",
author = "M.M. Lipkovich and A.L. Fradkov",
year = "2015",
doi = "10.1134/S0005117915050069",
language = "English",
volume = "76",
pages = "801--808",
journal = "Automation and Remote Control",
issn = "0005-1179",
publisher = "МАИК {"}Наука/Интерпериодика{"}",
number = "5",

}

RIS

TY - JOUR

T1 - About the necessity of Popov criterion for a special Lyapunov function existence for the systems with multiple nonlinearities

AU - Lipkovich, M.M.

AU - Fradkov, A.L.

PY - 2015

Y1 - 2015

N2 - © 2015, Pleiades Publishing, Ltd. Necessary and sufficient conditions for existence of Lyapunov function from the class “quadratic form plus integral of nonlinearity” (Lyapunov-Lurie function) for systems with several nonlinearities are considered. It is assumed that the nonlinearity graphs belong to the infinite sectors, i.e., belong to the union of the first and third quadrants in the plane. It is proven that Popov criterion is necessary and sufficient for existence of Lyapunov-Lurie function if the relative degree of the linear part is greater than one. The proof is based on the result concerning losslessness of the S-procedure for several respective quadratic constraints.

AB - © 2015, Pleiades Publishing, Ltd. Necessary and sufficient conditions for existence of Lyapunov function from the class “quadratic form plus integral of nonlinearity” (Lyapunov-Lurie function) for systems with several nonlinearities are considered. It is assumed that the nonlinearity graphs belong to the infinite sectors, i.e., belong to the union of the first and third quadrants in the plane. It is proven that Popov criterion is necessary and sufficient for existence of Lyapunov-Lurie function if the relative degree of the linear part is greater than one. The proof is based on the result concerning losslessness of the S-procedure for several respective quadratic constraints.

U2 - 10.1134/S0005117915050069

DO - 10.1134/S0005117915050069

M3 - Article

VL - 76

SP - 801

EP - 808

JO - Automation and Remote Control

JF - Automation and Remote Control

SN - 0005-1179

IS - 5

ER -

ID: 3969486