Explicit general solution of planar linear discrete systems with constant coefficients and weak delays

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F13%3APU102874" target="_blank" >RIV/00216305:26110/13:PU102874 - isvavai.cz</a>
Result on the web
<a href="https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2013-50" target="_blank" >https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2013-50</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1186/1687-1847-2013-50" target="_blank" >10.1186/1687-1847-2013-50</a>

Result language
angličtina
Original language name
Explicit general solution of planar linear discrete systems with constant coefficients and weak delays
Original language description
In this paper, planar linear discrete systems with constant coefficients and two delays $$ x(k+1)=Ax(k)+Bx(k-m)+Cx(k-n) $$ are considered where $kinbZ_0^{infty}:={0,1,dots,infty}$, $xcolon bZ_0^{infty}tomathbb{R}^2$, $m>n>0$ are fixed integers and $A=(a_{ij})$, $B=(b_{ij})$ and $C=(c_{ij})$ are constant $2times 2$ matrices. It is assumed that the system considered system is one with weak delays. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In this case, after several steps, the space of solutions with a given starting dimension $2(m+1)$ is pasted into a space with a dimension less than the starting one. In a sense, this situation is analogous to one known in the theory of linear differential systems with constant coefficients and weak delays when the initially infinite dimensional space of solutions on the initial interval turns (after several steps) into a finite dimensional set of solutions. For every possible case, explicit general solutions are constructed and, finally, results on the dimensionality of the space of solutions are obtained.
Czech name
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Czech description
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Project
<a href="/en/project/ED2.1.00%2F03.0097" target="_blank" >ED2.1.00/03.0097: AdMaS - Advanced Materials, Structures and Technologies</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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