TY  - JOUR
ID  - Diblík2025
LB  - Diblík2025
AU  - Diblík, Josef
TI  - Representation of solutions of linear discrete systems with constant coefficients and with delays
ST  - Representation of solutions of linear discrete systems with constant coefficients and with delays
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2025
VL  - 45
IS  - 2
SP  - 145
EP  - 177
DO  - https://doi.org/10.7494/OpMath.2025.45.2.145
UR  - https://doi.org/10.7494/OpMath.2025.45.2.145
AB  - The paper surveys the results achieved in representing solutions of linear non-homogeneous discrete systems with constant coefficients and with delays and their fractional variants by using special matrices called discrete delayed-type matrices. These are used to express solutions of initial problems in a closed and often simple form. Then, results are briefly discussed achieved by such representations of solutions in stability, controllability and other fields. In addition, a similar topic is dealt with concerning linear non-homogeneous differential equations with delays and their variants. Moreover, some comments are given to this parallel direction pointing some important moments in the developing this theory. An outline of future perspectives in this direction is discussed as well.
KW  - discrete linear system
KW  - constants coefficients
KW  - delay
KW  - discrete matrix functions
KW  - representation of solutions
KW  - commutative matrices
KW  - non-commutative matrices
KW  - controllability
SN  - 1232-9274
ER  -