Weakly Delayed Systems of Linear Discrete Equations in $mathbb{R}^3$

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F18%3APU138560" target="_blank" >RIV/00216305:26110/18:PU138560 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.vutbr.cz/studenti/zav-prace?zp_id=112186" target="_blank" >https://www.vutbr.cz/studenti/zav-prace?zp_id=112186</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Weakly Delayed Systems of Linear Discrete Equations in $mathbb{R}^3$

Popis výsledku v původním jazyce

The present thesis deals with the construction of a general solution of weakly delayed systems of linear discrete equations in ${mathbb R}^3$ of the form begin{equation*} x(k+1)=Ax(k)+Bx(k-m) end{equation*} where $m>0$ is a positive integer, $xcolon bZ_{-m}^{infty}tobR^3$, $bZ_{-m}^{infty} := {-m, -m+1, dots, infty}$, $kinbZ_0^{infty}$, $A=(a_{ij})$ and $B=(b_{ij})$ are constant $3times 3$ matrices. The characteristic equations of weakly delayed systems are identical with those of the same systems but without delayed terms. The criteria ensuring that a system is weakly delayed are developed and then specified for every possible case of the Jordan form of matrix $A$. The system is solved by transforming it into a higher-dimensional system but without delays begin{equation*} y(k+1)=mathcal{A}y(k), end{equation*} where ${mathrm{dim}} y = 3(m+1)$. Using methods of linear algebra, it is possible to find the Jordan forms of $mathcal{A}$ depending on the eigenvalues of matrices $A$ an

Název v anglickém jazyce

Weakly Delayed Systems of Linear Discrete Equations in $mathbb{R}^3$

Popis výsledku anglicky

The present thesis deals with the construction of a general solution of weakly delayed systems of linear discrete equations in ${mathbb R}^3$ of the form begin{equation*} x(k+1)=Ax(k)+Bx(k-m) end{equation*} where $m>0$ is a positive integer, $xcolon bZ_{-m}^{infty}tobR^3$, $bZ_{-m}^{infty} := {-m, -m+1, dots, infty}$, $kinbZ_0^{infty}$, $A=(a_{ij})$ and $B=(b_{ij})$ are constant $3times 3$ matrices. The characteristic equations of weakly delayed systems are identical with those of the same systems but without delayed terms. The criteria ensuring that a system is weakly delayed are developed and then specified for every possible case of the Jordan form of matrix $A$. The system is solved by transforming it into a higher-dimensional system but without delays begin{equation*} y(k+1)=mathcal{A}y(k), end{equation*} where ${mathrm{dim}} y = 3(m+1)$. Using methods of linear algebra, it is possible to find the Jordan forms of $mathcal{A}$ depending on the eigenvalues of matrices $A$ an

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů