Publication detail

# Construction of the general solution of planar linear discrete systems with constant coefficients and weak delay

DIBLÍK, J. KHUSAINOV, D. ŠMARDA, Z.

Original Title

Construction of the general solution of planar linear discrete systems with constant coefficients and weak delay

English Title

Construction of the general solution of planar linear discrete systems with constant coefficients and weak delay

Type

journal article

Language

en

Original Abstract

Planar linear discrete systems with constant coefficients and weak delay are considered. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In this case, the space of solutions with a given starting dimension is pasted after several steps into a space with dimension less than the starting one. In a sense this situation copies an analogous one known from the theory of linear differential systems with constant coefficients and weak delay when the initially infinite dimensional space of solutions on the initial interval on a reduced interval, turns, after several steps, into a finite dimensional set of solutions. For every possible case, general solutions are constructed and, finally, results on the dimensionality of the space of solutions are deduced.

English abstract

Planar linear discrete systems with constant coefficients and weak delay are considered. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In this case, the space of solutions with a given starting dimension is pasted after several steps into a space with dimension less than the starting one. In a sense this situation copies an analogous one known from the theory of linear differential systems with constant coefficients and weak delay when the initially infinite dimensional space of solutions on the initial interval on a reduced interval, turns, after several steps, into a finite dimensional set of solutions. For every possible case, general solutions are constructed and, finally, results on the dimensionality of the space of solutions are deduced.

Keywords

planar linear discrete system

RIV year

2009

Released

27.11.2009

Pages from

1

Pages to

18

Pages count

18

BibTex

```
@article{BUT48938,
author="Josef {Diblík} and Denys {Khusainov} and Zdeněk {Šmarda}",
title="Construction of the general solution of planar linear discrete systems with constant coefficients and weak delay",
annote="Planar linear discrete systems with constant coefficients and weak delay are considered. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In this case, the space of solutions with a given starting dimension
is pasted after several steps into a space with dimension less than the starting one. In a sense this situation copies an analogous one known from the theory of linear differential systems with constant coefficients and weak delay when the initially infinite dimensional space of solutions on the initial interval on a reduced interval, turns, after several steps, into a finite dimensional set of solutions. For every possible case, general solutions are constructed and, finally, results on the dimensionality of the space of solutions are deduced.",
chapter="48938",
journal="Advances in Difference Equations",
number="3",
volume="2009",
year="2009",
month="november",
pages="1--18",
type="journal article"
}
```