On counter-examples to Aizerman and Kalman conjectures
Igor Boiko, Н. В. Кузнецов, R. N. Mokaev, T. N. Mokaev, M. V. Yuldashev, R. V. Yuldashev
Abstract
Counter-examples to Aizerman's and Kalman's conjectures are considered. Investigation of the behaviour in the vicinity of the origin and at a distance from the origin is done. The simultaneous existence of both: a limit cycle and asymptotic or finite-time convergence is proved through the LPRS method and the Lyapunov method, respectively. Conclusions regarding the complex behaviour of these nonlinear dynamic systems are given.
Topics & Concepts
MathematicsConvergence (economics)Kalman filterLimit (mathematics)Nonlinear systemApplied mathematicsCounterexampleLyapunov functionLimit cycleControl theory (sociology)Calculus (dental)Mathematical analysisComputer sciencePhysicsDiscrete mathematicsControl (management)StatisticsArtificial intelligenceEconomicsQuantum mechanicsDentistryEconomic growthMedicineAdvanced Differential Equations and Dynamical SystemsMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Dynamics and Pattern Formation