TY - JOUR
N2 - 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.
JO - Archives of Control Sciences
L1 - http://www.czasopisma.pan.pl/Content/104500/PDF/acsc-2016-0030.pdf
L2 - http://www.czasopisma.pan.pl/Content/104500
PY - 2016
IS - No 4
A1 - Kaczorek, Tadeusz
PB - Committee of Automatic Control and Robotics PAS
JF - Archives of Control Sciences
DA - 2016
T1 - Analysis and comparison of the stability of discrete-time and continuous-time linear systems
UR - http://www.czasopisma.pan.pl/dlibra/docmetadata?id=104500
DOI - 10.1515/acsc-2016-0030
ER -