Search results for "Kalman conjecture"
showing 2 items of 2 documents
Counterexamples to the Kalman Conjectures
2018
In the paper counterexamples to the Kalman conjecture with smooth nonlinearity basing on the Fitts system, that are periodic solution or hidden chaotic attractor are presented. It is shown, that despite the fact that Kalman’s conjecture (as well as Aizerman’s) turned out to be incorrect in the case of n > 3, it had a huge impact on the theory of absolute stability, namely, the selection of the class of nonlinear systems whose stability can be studied with linear methods. peerReviewed
Coexistence of hidden attractors and multistability in counterexamples to the Kalman conjecture
2019
The Aizerman and Kalman conjectures played an important role in the theory of global stability for control systems and set two directions for its further development – the search and formulation of sufficient stability conditions, as well as the construction of counterexamples for these conjectures. From the computational perspective the latter problem is nontrivial, since the oscillations in counterexamples are hidden, i.e. their basin of attraction does not intersect with a small neighborhood of an equilibrium. Numerical calculation of initial data of such oscillations for their visualization is a challenging problem. Up to now all known counterexamples to the Kalman conjecture were const…