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.
Topics
Computational methods
REFERENCES
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.
10.
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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