Frequency-Domain Analysis of a Keldysh-Like System

I. M. Boiko; N. V. Kuznetsov; R. N. Mokaev; E. D. Akimova

doi:10.1002/rnc.70162

Frequency-Domain Analysis of a Keldysh-Like System

I. M. Boiko
, N. V. Kuznetsov
, R. N. Mokaev
, E. D. Akimova

Saint-Petersburg State University
Institute for Problems in Mechanical Engineering RAS

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

Abstract

Complex dynamics of the system, revealing flutter and first presented by M. Keldysh, is analyzed in the paper in the frequency domain, through the describing function method. Motivated by this analysis, a system with similar behavior, but suitable for the exact frequency-domain analysis through the locus of a perturbed relay system (LPRS) method, is analyzed after that. The undertaken analysis shows many interesting phenomena, which include two limit cycles, orbitally stable and unstable, equilibria, and sliding mode. The undertaken analysis allows us to identify, with a high degree of confidence, the key factors leading to the complex motions in the original and transformed dynamics.

Original language	British English
Pages (from-to)	671-682
Number of pages	12
Journal	International Journal of Robust and Nonlinear Control
Volume	36
Issue number	2
DOIs	https://doi.org/10.1002/rnc.70162
State	Published - 25 Jan 2026

Keywords

convergence to rest segment
nonlinear system
orbital stability
periodic solutions

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10.1002/rnc.70162

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title = "Frequency-Domain Analysis of a Keldysh-Like System",

abstract = "Complex dynamics of the system, revealing flutter and first presented by M. Keldysh, is analyzed in the paper in the frequency domain, through the describing function method. Motivated by this analysis, a system with similar behavior, but suitable for the exact frequency-domain analysis through the locus of a perturbed relay system (LPRS) method, is analyzed after that. The undertaken analysis shows many interesting phenomena, which include two limit cycles, orbitally stable and unstable, equilibria, and sliding mode. The undertaken analysis allows us to identify, with a high degree of confidence, the key factors leading to the complex motions in the original and transformed dynamics.",

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AU - Mokaev, R. N.

AU - Akimova, E. D.

PY - 2026/1/25

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N2 - Complex dynamics of the system, revealing flutter and first presented by M. Keldysh, is analyzed in the paper in the frequency domain, through the describing function method. Motivated by this analysis, a system with similar behavior, but suitable for the exact frequency-domain analysis through the locus of a perturbed relay system (LPRS) method, is analyzed after that. The undertaken analysis shows many interesting phenomena, which include two limit cycles, orbitally stable and unstable, equilibria, and sliding mode. The undertaken analysis allows us to identify, with a high degree of confidence, the key factors leading to the complex motions in the original and transformed dynamics.

AB - Complex dynamics of the system, revealing flutter and first presented by M. Keldysh, is analyzed in the paper in the frequency domain, through the describing function method. Motivated by this analysis, a system with similar behavior, but suitable for the exact frequency-domain analysis through the locus of a perturbed relay system (LPRS) method, is analyzed after that. The undertaken analysis shows many interesting phenomena, which include two limit cycles, orbitally stable and unstable, equilibria, and sliding mode. The undertaken analysis allows us to identify, with a high degree of confidence, the key factors leading to the complex motions in the original and transformed dynamics.

KW - convergence to rest segment

KW - nonlinear system

KW - orbital stability

KW - periodic solutions

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Frequency-Domain Analysis of a Keldysh-Like System

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Keywords

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