TY - GEN

T1 - Analytical-numerical methods for investigation of hidden oscillations in nonlinear control systems

AU - Leonov, G. A.

AU - Kuznetsov, N. V.

N1 - Funding Information: ⋆The work was supported by Academy of Finland, Ministry of Education and Science of Russian Federation, St.Petrsburg State University, and RFBR.

PY - 2011

Y1 - 2011

N2 - The method of harmonic linearization, numerical methods, and the applied bifurcation theory together discover new opportunities for analysis of oscillations of control systems. In the present survey analytical-numerical algorithms for hidden oscillation localization are discussed. Examples of hidden attractor localization in Chua's circuit and counterexamples construction to Aizerman's conjecture and Kalman's conjecture are considered.

AB - The method of harmonic linearization, numerical methods, and the applied bifurcation theory together discover new opportunities for analysis of oscillations of control systems. In the present survey analytical-numerical algorithms for hidden oscillation localization are discussed. Examples of hidden attractor localization in Chua's circuit and counterexamples construction to Aizerman's conjecture and Kalman's conjecture are considered.

KW - Absolute stability

KW - Aizerman problem

KW - Chua's circuit

KW - Describing function method

KW - Harmonic balance

KW - Harmonic linearization

KW - Hidden attractor

KW - Hidden oscillation

KW - Kalman problem

KW - Localization

UR - http://www.scopus.com/inward/record.url?scp=84866756426&partnerID=8YFLogxK

U2 - 10.3182/20110828-6-IT-1002.03315

DO - 10.3182/20110828-6-IT-1002.03315

M3 - Conference contribution

AN - SCOPUS:84866756426

SN - 9783902661937

T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)

SP - 2494

EP - 2505

BT - Proceedings of the 18th IFAC World Congress

PB - International Federation of Automatic Control

ER -