TY  - JOUR
ID  - Majewski2017
LB  - Majewski2017
AU  - Majewski, Marek
TI  - Control system defined by some integral operator
ST  - Control system defined by some integral operator
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 2
SP  - 313
EP  - 325
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.2.313
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.2.313
AB  - 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.
KW  - Volterra equation
KW  - implicit function theorem
KW  - sensitivity
SN  - 1232-9274
ER  -