This investigation is a joint work with Josef Diblík (Brno
University of Technology, Czech Republic), Denys Khusainov (Kiev
National University, Ukraine) and Andrii Sirenko (Kiev National
University, Ukraine).
Consider the so-called linear interval difference systems
with delay
\begin{equation*}\tag{1} x\left( {k+1} \right)=\left( {A+\Delta A(k)}
\right)x\left( k \right)+\left( {B+\Delta B(k)} \right)x\left( {k-m}
\right), \quad k=1,2,\dots
\end{equation*}
Where \(A,B\) are constant matrices, \(\Delta A(k)=\left\{ {\Delta
a_{ij}(k)} \right\}\), \(\Delta B=\left\{ {\Delta b_{ij}(k) } \right\}
\quad i,j=1,2,\dots,n \) are matrices whose coefficients can take
their values from some preassigned intervals
\begin{equation*}\label{eq28}
\left| {\Delta a_{ij}(k) }
\right|\leq \alpha _{ij}, \quad \left| {\Delta
b_{ij}(k) } \right|\leq \beta _{ij}, \quad i,j=1,2,\dots,n ,
\end{equation*}
and \(\alpha _{ij}\geq 0\), \(\beta _{ij}\geq 0\) are constants.
We formulate a definition of interval stability and give sufficient
conditions guaranteeing interval stability of the system (1).
Estimation of convergence of solutions is derived as well.
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