Algorithm for construction of counterexamples to Aizerman's and Kalman's conjectures

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 43, Issue 11 PART 1, 2010, Pages 24-28

  Bragin, V O ^a   Kuznetsov, N V ^a   Leonov, G A ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

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

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; PERIODIC SOLUTION;

NUMERICAL METHODS;

EID: 84880372948     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20100826-3-tr-4016.00008     Document Type: Conference Paper

References (13)

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3. N.E. Barabanov. On the Kalman problem Sib. Math. J., 29(3), 333-341, 1988.
4. 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, N 3. 337-379, 1996.
5. R.E. Fitts. Two counterexamples to Aizerman's conjecture Trans. IEEE., V. AC-11, N3, 553-556, 1966.
6. A.A. Glutsyuk. 1997. Meetings of the Moscow Mathematical Society. Russian mathematical surveys, 53:2, 413-417, 1998.
7. R.E. Kalman. Physical and Mathematical mechanisms of instability in nonlinear automatic control systems Transactions of ASME, 79:3, 553-566, 1957.
8. G.A. Leonov, I.M. Burkin, A.I. Shepeljavyi. Frequency methods in oscillation theory. Kluwer Acad. Publ., 1996.
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10. G.A. Leonov. Effective methods for periodic oscillations search in dynamical systems. App. math. & mech., Vol. 74, Iss. 1, 37-73, 2010.
11. 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.
12. 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.
13. G. Meisters. A Biography of the Markus-Yamabe Conjecture, 1996. www.math.unl.edu/gmeisters1/papers/HK1996.pdf.