The paper considers a delayed system of discrete equations
an initial problem x(k) = φ(k), k = −m, …, 0 and prescribed impulses x(k + 1) = Cx(k + 1 − 0) + Jk + 1, k = 0, 1, …, where A, B and C are regular square matrices satisfying ACB = BCA, f and Jk + 1 are column vectors, m > 0 is an integer and x is an unknown vector. A formula is derived for a solution satisfying the initial problem and the prescribed impulses.
1.
B.
Morávková
, Ph. D. Thesis,
Brno University of Technology
,
Brno, Czech Republic
,
2014
.
2.
J.
Diblík
, and
D.Ya.
Khusainov
,
Adv. Diff. Equ.
,
2006
(
2006
), Art. ID 80825,
1
13
.
3.
J.
Diblík
, and
D.Ya.
Khusainov
,
J. Math. Anal. Appl.
,
318
(
2006
),
63
76
.
4.
J.
Diblík
, and
B.
Morávková
,
Adv. Difference Equ.
2013
,
2013
:139,
18
pp.
5.
J.
Diblík
, and
B.
Morávková
,
Abstr. Appl. Anal.
2014
, Art. ID 320476,
19
pp.
6.
J.
Diblík
,
D.Ya.
Khusainov
, and
M.
Růžičková
,
SIAM J. Control Optim.
,
47
, no.
3
, pp.
1140
1149
,
2008
.
7.
A.
Boichuk
,
J.
Diblík
,
D.Ya.
Khusainov
, and
M.
Růžičková
,
Nonlinear Anal.
72
, no.
5
,
2251
2258
,
2010
.
8.
J.
Diblík
,
M.
Fečkan
, and
M.
Pospíšil
,
SIAM J. Control Optim.
52
(
2014
), no.
3
,
1745
1760
.
9.
M.
Pospıšil
,
Appl. Math. Comput.
294
(
2017
),
180
194
.
10.
M.
Medved’
, and
M.
Pospíšil
,
Commun. Appl. Anal.
17
(
2013
), no.
1
,
21
45
.
11.
Z.
You
,
M.
Fečkan
, and
JinRong
Wang
,
J. Comput. Appl. Math.
378
(
2020
),
112939
, 16 pp.
12.
N.
Mahmudov
,
Electron. J. Qual. Theory Differ. Equ.
2020
, Paper No. 53,
12
pp.
13.
J.
Diblík
, and
K.
Mencáková
,
Appl. Math. Lett.
105
(
2020
),
106309
, 7 pp.
14.
R.
Medina
, and
C.
Martinez
,
Internat. J. Robust Nonlinear Control
25
(
2015
), no.
4
,
527
541
.
15.
M.
Li
,
A.
Debbouche
, and
JinRong
Wang
,
Math. Methods Appl. Sci.
41
(
2018
), no.
18
,
8906
8914
.
16.
Ch.
Liang
,
W.
Wei
, and
JinRong
Wang
,
Adv. Difference Equ.
2017
, Paper No. 131,
17
pp.
17.
Z.
Zhongli
,
JinRong
Wang
, and
D.
O’Regan
, D.
Bull. Braz. Math. Soc. (N.S.
)
50
(
2019
), no.
2
,
457
479
.
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