Open AccessOn constructing single-input non-autonomous systems of full rank
Author(s) -
D. N. Andreieva,
Svetlana Yu. Ignatovich
Publication year - 2018
Publication title -
vìsnik harkìvsʹkogo nacìonalʹnogo unìversitetu ìmenì v.n. karazìna. serìâ: matematika, prikladna matematika ì mehanìka
Language(s) - English
Resource type - Journals
eISSN - 2523-4641
pISSN - 2221-5646
DOI - 10.26565/2221-5646-2018-88-04
Subject(s) - rank (graph theory) , vector field , nonlinear system , mathematics , class (philosophy) , field (mathematics) , differential (mechanical device) , mathematical analysis , pure mathematics , physics , combinatorics , discrete mathematics , computer science , geometry , quantum mechanics , artificial intelligence , thermodynamics
For a nonlinear system of differential equations $\dot x=f(x)$, a method of constructing a system of full rank $\dot x=f(x)+g(x)u$ is studied for vector fields of the class $C^k$, $1\le k<\infty$, in the case when $f(x)\not=0$. A method for constructing a non-autonomous system of full rank is proposed in the case when the vector field $f(x)$ can vanish.