Solutions of Delayed Linear Discrete Two-Dimensional Systems With Constant Coefficients in the Case of Single Zero Eigenvalue of the Matrix of Nondelayed Terms

Solutions of Delayed Linear Discrete Two-Dimensional Systems With Constant Coefficients in the Case of Single Zero Eigenvalue of the Matrix of Nondelayed Terms

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Linear discrete two-dimensional systems of the form y(n + 1) = Cy(n) + Dy(n-ℓ), n≥0, where n is an independent variable and y: {-ℓ, -ℓ + 1,...}→ℝ2 is an unknown function, are considered provided that e is a positive fixed integer and the coefficients of the 2 by 2 constant matrices C and D satisfy conditions known for the so-called weakly delayed discrete systems. General solutions of such systems are constructed assuming that the matrix C has two real eigenvalues, with exactly one of them equaling zero. A problem is discussed on the minimal number of initial values necessary to define a solution and the number of independent arbitrary constants in the general solution.

Linear discrete two-dimensional systems of the form y(n + 1) = Cy(n) + Dy(n-ℓ), n≥0, where n is an independent variable and y: {-ℓ, -ℓ + 1,...}→ℝ2 is an unknown function, are considered provided that e is a positive fixed integer and the coefficients of the 2 by 2 constant matrices C and D satisfy conditions known for the so-called weakly delayed discrete systems. General solutions of such systems are constructed assuming that the matrix C has two real eigenvalues, with exactly one of them equaling zero. A problem is discussed on the minimal number of initial values necessary to define a solution and the number of independent arbitrary constants in the general solution.

Discrete system, Delay, Zero Eigenvalue, Constant coefficients.

Discrete system, Delay, Zero Eigenvalue, Constant coefficients.

DIBLÍK, J.; HARTMANOVÁ, M.

2026

11.09.2025

American Institute of Physics

USA

9780735452459

AIP Conf. Proc. 3315, 260002 (2025)

AIP conference proceedings

Spojené státy americké

260005-1

260005-4

4

https://pubs.aip.org/aip/acp/article-abstract/3315/1/260005/3363140/Solutions-of-delayed-linear-discrete-two?redirectedFrom=fulltext