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DIBLÍK, J. HALFAROVÁ, H. ŠAFAŘÍK, J.
Original Title
Formulas for the general solution of weakly delayed planar linear discrete systems with constant coefficients and their analysis
Type
journal article in Web of Science
Language
English
Original Abstract
The paper is concerned with weakly delayed linear discrete homogeneous planar systems with constant coefficients. By the method of Z-transform, formulas for the general solutions, dependent on the Jordan forms of the matrix of non-delayed linear terms, are derived and the influence is analyzed of the delay on the form of the general solutions. It is shown that, after several steps, the general solutions depend only on two arbitrary parameters which are linear combinations of the initial values. This property is used to prove results on conditional stability. Linear discrete homogeneous planar systems without delay are found to have the same general solutions as the initial one. The results are illustrated by examples. Previous results are analyzed, commented and improved.
Keywords
Linear discrete system; Weakly delayed system; Jordan form; Planar system; Conditional stability
Authors
DIBLÍK, J.; HALFAROVÁ, H.; ŠAFAŘÍK, J.
Released
1. 10. 2019
Publisher
Elsevier
ISBN
0096-3003
Periodical
APPLIED MATHEMATICS AND COMPUTATION
Year of study
358
Number
10
State
United States of America
Pages from
363
Pages to
381
Pages count
18
URL
https://www.sciencedirect.com/science/article/pii/S0096300319302760?via%3Dihub
BibTex
@article{BUT157258, author="Josef {Diblík} and Hana {Boháčková} and Jan {Šafařík}", title="Formulas for the general solution of weakly delayed planar linear discrete systems with constant coefficients and their analysis", journal="APPLIED MATHEMATICS AND COMPUTATION", year="2019", volume="358", number="10", pages="363--381", doi="10.1016/j.amc.2019.03.068", issn="0096-3003", url="https://www.sciencedirect.com/science/article/pii/S0096300319302760?via%3Dihub" }