Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R^2

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R^2

Popis výsledku v původním jazyce

Two-dimensional linear discrete systems $x(k+1)=Ax(k)+sumlimits_{l=1}^{n}B^{l}x_{l}(k-m_{l}), kge 0$ are analyzed, where $m_{1}, m_{2},dots, m_{n}$ are constant integer delays, $0<m_{1}<m_{2}<dots<m_{n}$, $A, B^{1},dots, B^{n}$ are constant $2times 2$ matrices, $A=(a_{ij})$, $B^{l}=(b^l_{ij})$, $i,j=1,2$, $l=1,2,dots,n$ and $xcolon {-m_n,-m_n+1,dots}to R^2$. Under the assumption that the system is weakly delayed, the asymptotic behavior of its solutions is studied. Asymptotic formulas describing the solutions are derived as well as sufficient conditions for conditional stability and asymptotic conditional stability.

Název v anglickém jazyce

Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R^2

Popis výsledku anglicky

Two-dimensional linear discrete systems $x(k+1)=Ax(k)+sumlimits_{l=1}^{n}B^{l}x_{l}(k-m_{l}), kge 0$ are analyzed, where $m_{1}, m_{2},dots, m_{n}$ are constant integer delays, $0<m_{1}<m_{2}<dots<m_{n}$, $A, B^{1},dots, B^{n}$ are constant $2times 2$ matrices, $A=(a_{ij})$, $B^{l}=(b^l_{ij})$, $i,j=1,2$, $l=1,2,dots,n$ and $xcolon {-m_n,-m_n+1,dots}to R^2$. Under the assumption that the system is weakly delayed, the asymptotic behavior of its solutions is studied. Asymptotic formulas describing the solutions are derived as well as sufficient conditions for conditional stability and asymptotic conditional stability.

Druh

O - Ostatní výsledky

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

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