@article{Kaczorek_Tadeusz_Analysis_2016,
author={Kaczorek, Tadeusz},
number={No 4},
howpublished={online},
journal={Archives of Control Sciences},
year={2016},
publisher={Committee of Automatic Control and Robotics PAS},
abstract={Abstract
The asymptotic stability of discrete-time and continuous-time linear systems described by the equations xi+1 = Ākxi and x(t) = Akx(t) for k being integers and rational numbers is addressed. Necessary and sufficient conditions for the asymptotic stability of the systems are established. It is shown that: 1) the asymptotic stability of discrete-time systems depends only on the modules of the eigenvalues of matrix Āk and of the continuous-time systems depends only on phases of the eigenvalues of the matrix Ak, 2) the discrete-time systems are asymptotically stable for all admissible values of the discretization step if and only if the continuous-time systems are asymptotically stable, 3) the upper bound of the discretization step depends on the eigenvalues of the matrix A.},
title={Analysis and comparison of the stability of discrete-time and continuous-time linear systems},
doi={10.1515/acsc-2016-0030},
}