@Article{Majewski2017,
author = "Majewski, Marek",
title = "Control system defined by some integral operator",
journal = "Opuscula Math.",
year = "2017",
volume = "37",
number = "2",
pages = "313--325",
doi = "http://dx.doi.org/10.7494/OpMath.2017.37.2.313",
url = "http://dx.doi.org/10.7494/OpMath.2017.37.2.313",
abstract = "In the paper we consider a nonlinear control system governed by the Volterra integral operator. Using a version of the global implicit function theorem we prove that the control system under consideration is well-posed and robust, i.e. for any admissible control \(u\) there exists a uniquely defined trajectory \(x_{u}\) which continuously depends on control \(u\) and the operator \(u\mapsto x_{u}\) is continuously differentiable. The novelty of this paper is, among others, the application of the Bielecki norm in the space of solutions which allows us to weaken standard assumptions.",
keywords = "Volterra equation, implicit function theorem, sensitivity",
issn = "1232-9274"
}