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Representation of solutions of discrete delayed system \(x(k+1)=Ax(k)+Bx(k-m)+f(k)\) with commutative matrices. (English) Zbl 1094.39002

A non-autonomous delayed matrix difference equation is considered. Under conditions on the matrix coefficients, an explicit formula is presented for the solution of the initial-value problem.

MSC:

39A10 Additive difference equations
39B42 Matrix and operator functional equations
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[1] Baštinec, J.; Diblík, J., One case of appearance of positive solutions of delayed discrete equations, Appl. Math., 48, 429-436 (2003) · Zbl 1099.39001
[2] Baštinec, J.; Diblík, J., Subdominant positive solutions of the discrete equation \(\Delta u(k + n) = - p(k) u(k)\), Abstr. Appl. Anal., 6, 461-470 (2004) · Zbl 1078.39004
[3] Boichuk, A.; Růžičková, M., Solutions of nonlinear difference equations bounded on the whole line, Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math., 13, 45-60 (2002) · Zbl 1106.39302
[4] Čermák, J., The asymptotic of solutions for a class of delay differential equations, Rocky Mountain J. Math., 33, 775-786 (2003) · Zbl 1050.34119
[5] Diblík, J., Anti-Lyapunov method for systems of discrete equations, Nonlinear Anal., 57, 1043-1057 (2004) · Zbl 1065.39008
[6] Elaydi, S. N., An Introduction to Difference Equations (1999), Springer · Zbl 0930.39001
[7] Györi, I.; Ladas, G., Oscillation Theory of Delay Differential Equations (1991), Clarendon · Zbl 0780.34048
[8] Hale, J. K.; Lunel, S. M.V., Introduction to Functional Differential Equations (1993), Springer · Zbl 0787.34002
[9] Khusainov, D. Ya.; Shuklin, G. V., Linear autonomous time-delay system with permutation matrices solving, Stud. Univ. Žilina Math. Ser., 17, 101-108 (2003) · Zbl 1064.34042
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