@ARTICLE{Kaczorek_Tadeusz_Analysis_2016, author={Kaczorek, Tadeusz}, number={No 4}, journal={Archives of Control Sciences}, howpublished={online}, 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}, URL={http://www.journals.pan.pl/Content/104500/PDF/acsc-2016-0030.pdf}, doi={10.1515/acsc-2016-0030}, }