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AIZERMANS CONJECTURE

• Aizerman's conjecture

In nonlinear control, Aizerman's conjecture or Aizerman problem states that a linear system in feedback with a sector nonlinearity would be stable if

Aizerman's conjecture

Aizerman's_conjecture

• Kalman's conjecture

Disproved conjecture

stability. Kalman's conjecture is a strengthening of Aizerman's conjecture and is a special case of Markus–Yamabe conjecture. This conjecture was proven false

Kalman's conjecture

Kalman's_conjecture

• Nonlinear control

Control theory for nonlinear or time-variant systems

well-known wrong conjectures on the absolute stability problem: The Aizerman's conjecture The Kalman's conjecture. Graphically, these conjectures can be interpreted

Nonlinear control

Nonlinear_control

• Markus–Yamabe conjecture

In mathematics, the Markus–Yamabe conjecture is a conjecture on global asymptotic stability. If the Jacobian matrix of a dynamical system at a fixed point

Markus–Yamabe conjecture

Markus–Yamabe_conjecture

• Hidden attractor

equilibrium, which is stable e.g. the counterexamples to Aizerman's conjecture (1949) and Kalman's conjecture (1957) on the monostability of nonlinear control

Hidden attractor

Hidden_attractor

• William F. Egan

Author

stability and the pull-in range in the space of parameters is trivial). The conjecture can be found in various later publications, see e.g. and for type II CP-PLL

William F. Egan

William_F._Egan

• Nikolay V. Kuznetsov

Russian scientist

loops, nonlinear analysis of the CP-PLL and validation of the Gardner conjecture, counterexamples with self-excited and hidden attractors to the classical

Nikolay V. Kuznetsov



Nikolay_V._Kuznetsov

• Describing function

same (simple) way. Also, in the case where the conditions for Aizerman's or Kalman conjectures are fulfilled, there are no periodic solutions by describing

Describing function

Describing_function

• Perceptron

Algorithm for supervised learning of binary classifiers

learn an XOR function. It is often incorrectly believed that they also conjectured that a similar result would hold for a multi-layer perceptron network

Perceptron

Perceptron

• Chua's circuit

Electronic circuit that behaves chaotically

implementation of Chua circuit is switched on at the zero initial data, thus a conjecture was that the chaotic behavior is possible only in the case of unstable

Chua's circuit



Chua's_circuit

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