Showing papers on "Aizerman's conjecture published in 2014"
TL;DR: In this article, the generalized Aizerman conjecture holds for positive linear systems and an explicit criterion for exponential stability is presented for systems with nonlinear time-varying perturbations.
Abstract: SUMMARY
General nonlinear time-varying differential systems are considered. An explicit criterion for exponential stability is presented. Furthermore, an explicit robust stability bound for systems subjected to nonlinear time-varying perturbations is given. In particular, it is shown that the generalized Aizerman conjecture holds for positive linear systems. Some examples are given to illustrate obtained results.Copyright © 2012 John Wiley & Sons, Ltd.
10 citations
TL;DR: In this article, the Lowner differential equation is used to obtain sufficient conditions in the two-functional conjecture and compare the sufficient conditions with necessary conditions, and then the necessary conditions are compared with sufficient conditions.
Abstract: The two-functional conjecture says that if a function analytic and univalent in the unit disk maximizes and for two continuous linear functionals and , for any , then is a rotation of the Koebe function. We use the Lowner differential equation to obtain sufficient conditions in the two-functional conjecture and compare the sufficient conditions with necessary conditions.