Hidden oscillations in nonlinear control systems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 44, Issue 1 PART 1, 2011, Pages 2506-2510

  Kuznetsov, N V ^a,b   Leonov, G A ^a   Seledzhi, S M ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

Absolute stability; Aizerman problem; Describing function method; Harmonic balance; Harmonic linearization; Hidden oscillation; Kalman problem; Localization

Indexed keywords

BIFURCATION (MATHEMATICS); CONTROL SYSTEM ANALYSIS; HARMONIC ANALYSIS; LINEARIZATION;

ABSOLUTE STABILITY; AIZERMAN PROBLEM; DESCRIBING FUNCTION METHODS; HARMONIC BALANCE; HARMONIC LINEARIZATION; HIDDEN OSCILLATION; KALMAN PROBLEM; LOCALIZATION;

NUMERICAL METHODS;

EID: 84866748354     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20110828-6-IT-1002.03316     Document Type: Conference Paper

References (16)

1. M.A. Aizerman. On a problem concerning the stability "in the large" of dynamical systems. Russian mathematical surveys, Vol. 4, Iss. 4, 186-188, 1949.
2. N.E. Barabanov. On the Kalman problem Sib. Math. J., 29(3), 333-341, 1988.
3. J. Bernat, J. Llibre. Counterexample to Kalman and Markus-Yamabe conjectures in dimension larger than 3. Dynamics of Continuous, Discrete and Impulsive Systems, Vol. 2, N3. 337-379, 1996.
4. V.O. Bragin, N.V. Kuznetsov, G.A. Leonov. Algorithm for counterexamples construction for Aizerman's and Kalman's conjectures. Proceedings of 4th IFAC Workshop on Periodic Control System. 2010. (DOI: 10.3182/20100826-3-TR-4016. 00008)
5. N.P. Erugin. A Problem in the theory of stability of automatic control systems. Applied Maht. & Mech., 5, 620-628, 1952.
6. R.E. Kalman. Physical and Mathematical mechanisms of instability in nonlinear automatic control systems Transactions of ASME, 79:3, 553-566, 1957.
7. N.N. Krasovsky. Theorems on the stability of motions determined by a system of two equations. Applied Maht. & Mech., 16(5), 547-554, 1952.
8. N.V. Kuznetsov, G.A. Leonov, V.I. Vagaitsev. Analyticalnumerical method for attractor localization of generalized Chua's system. Proceedings of 4th IFAC Workshop on Periodic Control System. 2010. (DOI: 10.3182/20100826-3-TR-4016. 00009)
9. S. Lefschetz. Stability of Nonlinear Control Systems.. Academic Press, NY-L, 1965.
10. G.A. Leonov, I.M. Burkin, A.I. Shepeljavyi. Frequency methods in oscillation theory. Kluwer Acad. Publ., 1996.
11. G.A. Leonov. On Aizerman problem. Automation and remote control, N7, 37-49, 2009.
12. G.A. Leonov. Effective methods for periodic oscillations search in dynamical systems. App. math. & mech., Vol. 74, Iss. 1, 37-73, 2010.
13. G.A. Leonov, V.O. Bragin, N.V. Kuznetsov. Algorithm for Constructing Counterexamples to the Kalman Problem. Doklady Mathematics, Vol. 82, No. 1, 540-542, 2010.
14. G.A. Leonov, V.I. Vagaitsev, N.V. Kuznetsov. Algorithm for localizing Chua attractors based on the harmonic linearization method. Doklady Mathematics, Vol. 82, No. 1, 663-666, 2010.
15. I.G. Malkin. On the stability of automatic control systems. Applied Maht. & Mech., 16(4), 495-499, 1952.
16. V.A. Pliss. Some Problems in the Theory of the Stability of Motion. Izd LGU, Leningrad, 1958.