Analysis and comparison of the stability of discrete-time and continuous-time linear systems
Divisions of PAS
<jats:title>Abstract</jats:title> <jats:p> The asymptotic stability of discrete-time and continuous-time linear systems described by the equations x<jats:sub>i+1</jats:sub> = Ā<jats:sup>k</jats:sup>x<jats:sub>i</jats:sub> and x(t) = A<jats:sup>k</jats:sup>x(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 Ā<jats:sup>k</jats:sup> and of the continuous-time systems depends only on phases of the eigenvalues of the matrix A<jats:sup>k</jats:sup>, 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.</jats:p>
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