Showing papers on "Aizerman's conjecture published in 2015"
TL;DR: A class of second-order discrete-time systems for which the Kalman conjecture is true provided the nonlinearity is odd, but false in general is discussed, which has strong implications for the analysis of saturated systems.
67 citations
TL;DR: An input-to-state stability theory, which subsumes results of circle criterion type, is developed in the context of continuous-time Lur’e systems, inspired by the complexified Aizerman conjecture.
Abstract: An input-to-state stability theory, which subsumes results of circle criterion type, is developed in the context of continuous-time Lur’e systems. The approach developed is inspired by the complexified Aizerman conjecture.
28 citations
15 Jul 2015
TL;DR: The discrete-time Kalman conjecture is shown to be false for systems of order two and above, which contrasts with continuoustime domain systems where the KalMan conjecture is true for third-order systems.
Abstract: In this paper, the discrete-time Kalman conjecture is shown to be false for systems of order two and above. Counterexamples are constructed. This contrasts with continuoustime domain systems where the Kalman conjecture is true for third-order systems.
21 citations
Posted Content•
TL;DR: In this article, an equivalent proposition of Brennan's conjecture was obtained, given two lower bounds of the conjecture, one connected with Schwarzian derivative and the other connected with a lower bound on the Schwarzian derivatives.
Abstract: In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the conjecture in some special conditions.