Solutions of linear discrete systems with a single delay and impulses

Solutions of linear discrete systems with a single delay and impulses

Paper in proceedings (conference paper)

The paper considers a delayed system of discrete equations x(k + 1) = Ax(k) + Bx(k − m) + f (k) , k = 0 , 1 , . . . , an initial problem x(k) = ϕ (k), k = −m, . . . , 0 and prescribed impulses x(k + 1) = Cx(k + 1 − 0) + J_{ k+ 1} , k = 0 , 1 , . . . , where A, B and C are regular square matrices satisfying ACB = BCA, f and J_{k+ 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.

The paper considers a delayed system of discrete equations x(k + 1) = Ax(k) + Bx(k − m) + f (k) , k = 0 , 1 , . . . , an initial problem x(k) = ϕ (k), k = −m, . . . , 0 and prescribed impulses x(k + 1) = Cx(k + 1 − 0) + J_{ k+ 1} , k = 0 , 1 , . . . , where A, B and C are regular square matrices satisfying ACB = BCA, f and J_{k+ 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.

discrete equation, delay, impulse; formula for solutions

discrete equation, delay, impulse; formula for solutions

MORÁVKOVÁ, B.; DIBLÍK, J.

2024

01.09.2023

American Institute of Physics

Melville (USA)

AIP Conference Proceedings, International Conference on Numerical Analysis and Applied Mathematics 2021, ICNAAM 2021

0094-243X

AIP conference proceedings

2849

1

United States of America

370003-1

370003-4

4

https://pubs-aip-org.ezproxy.lib.vutbr.cz/aip/acp/article/2849/1/370003/2909250/Solutions-of-linear-discrete-systems-with-a-single