Aizerman's conjecture
Encyclopedia
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.
Nonlinear control
Nonlinear control is the area of control engineering specifically involved with systems that are nonlinear, time-variant, or both. Many well-established analysis and design techniques exist for LTI systems ; however, one or both of the controller and the system under control in a general 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
Circle criterion
In nonlinear control, the circle criterion is an important theorem in showing the stability of nonlinear time-varying systems. It can be viewed as a generalization of the Nyquist stability criterion for LTI systems.-Overview:...
and Popov criterion.