Aizerman's conjecture

In nonlinear control, Aizerman's conjecture states that a linear system in feedback with a sector nonlinearity would be stable if the linear system is stable for any linear gain of the sector. This conjecture was proven false but led to the (valid) circle criterion and Popov criterion.^[1]

References

^ Atherton, D.P.; Siouris, G.M. (1977). "Nonlinear Control Engineering". Systems, Man and Cybernetics, IEEE Transactions on 7 (7): 567–568. doi:10.1109/TSMC.1977.4309773. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4309773. Retrieved 2008-06-30.

Further reading

Bragin V.O., Vagaitsev V.I., Kuznetsov N.V., Leonov G.A. (2011). "Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua's Circuits". Journal of Computer and Systems Sciences International 50 (4): 511–543. doi:10.1134/S106423071104006X.

External links

"Counterexamples to Aizerman's and Kalman's conjectures and DF method". http://www.math.spbu.ru/user/nk/PDF/Harmonic_balance_Absolute_stability.pdf.