TY - GEN

T1 - The birth of the global stability theory and the theory of hidden oscillations

AU - Kuznetsov, N. V.

AU - Lobachev, M. Y.

AU - Yuldashev, M. V.

AU - Yuldashev, R. V.

AU - Kudryashova, E. V.

AU - Kuznetsova, O. A.

AU - Rosenwasser, E. N.

AU - Abramovich, S. M.

N1 - Funding Information: *This survey is prepared for the invited session “History of nonlinear systems and control” at the European Control Conference, Saint Petersburg, 2020. The work is supported by the Leading Scientific Schools of Russia project NSh-2624.2020.1 (sections 1) and the Russian Science Foundation project 19-41-02002 (section 2-3) aNikolay V. Kuznetsov is with the Faculty of Mathematics and Mechanics, Saint Petersburg State University, Russia, with the Faculty of Mathematical Information Technology, University of Jyväskylä, Finland, with the Institute for Problems in Mechanical Engineering RAS, Russia nkuznetsov239@gmail.com bMikhail Y. Lobachev, Marat V. Yuldashev, Renat V. Yuldashev, Elena V. Kudryashova, Olga A. Kuznetsova are with the Faculty of Mathematics and Mechanics, Saint Petersburg State University, Russia cEfim N. Rosenwasser is with Saint Petersburg State Marine Technical University, Russia, a participant of the first IFAC World Congress in 1960 dSergei M. Abramovich is with State University of New York at Potsdam, USA Publisher Copyright: © 2020 EUCA. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/5

Y1 - 2020/5

N2 - The first mathematical problems of the global analysis of dynamical models can be traced back to the engineering problem of the Watt governor design. Engineering requirements and corresponding mathematical problems led to the fundamental discoveries in the global stability theory. Boundaries of global stability in the space of parameters are limited by the birth of oscillations. The excitation of oscillations from unstable equilibria can be easily analysed, while the revealing of oscillations not connected with equilibria is a challenging task being studied in the theory of hidden oscillations. In this survey, a brief history of the first global stability criteria development and corresponding counterexamples with hidden oscillations are discussed.

AB - The first mathematical problems of the global analysis of dynamical models can be traced back to the engineering problem of the Watt governor design. Engineering requirements and corresponding mathematical problems led to the fundamental discoveries in the global stability theory. Boundaries of global stability in the space of parameters are limited by the birth of oscillations. The excitation of oscillations from unstable equilibria can be easily analysed, while the revealing of oscillations not connected with equilibria is a challenging task being studied in the theory of hidden oscillations. In this survey, a brief history of the first global stability criteria development and corresponding counterexamples with hidden oscillations are discussed.

UR - http://www.scopus.com/inward/record.url?scp=85089293901&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85089293901

T3 - European Control Conference 2020, ECC 2020

SP - 769

EP - 774

BT - European Control Conference 2020, ECC 2020

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 19th European Control Conference, ECC 2020

Y2 - 12 May 2020 through 15 May 2020

ER -