On the number of arbitrary parameters in the general solution to a weakly delayed planar linear discrete system with constant coefficients

On the number of arbitrary parameters in the general solution to a weakly delayed planar linear discrete system with constant coefficients

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A planar linear discrete system with constant coefficients and two delays x(k + 1) = Ax(k) + Bx(k − m) + Cx(k − n) is considered where k ∈ Z. It is assumed that the system is weakly delayed and the eigenvalues of the matrix A are real and different. The formula for a general solution of the system is well-known and depends on 2(m + 1) initial values. This formula can be simplified to depend only on 2 arbitrary constants. A relation between the initial values and new arbitrary constants is given.

A planar linear discrete system with constant coefficients and two delays x(k + 1) = Ax(k) + Bx(k − m) + Cx(k − n) is considered where k ∈ Z. It is assumed that the system is weakly delayed and the eigenvalues of the matrix A are real and different. The formula for a general solution of the system is well-known and depends on 2(m + 1) initial values. This formula can be simplified to depend only on 2 arbitrary constants. A relation between the initial values and new arbitrary constants is given.

planar linear discrete system; constant coefficients; two delays; initial values

planar linear discrete system; constant coefficients; two delays; initial values

HALFAROVÁ, H.; DIBLÍK, J.; ŠAFAŘÍK, J.

2021

24.11.2020

American Institute of Physics

Melville (USA)

978-0-7354-4025-8

Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2019 (ICNAAM-2019)

0094-243X

AIP conference proceedings

2293

1

Spojené státy americké

340008-1

340008-4

4

https://aip.scitation.org/doi/abs/10.1063/5.0026615