http://popups.lib.uliege.be/1373-5411/index.php?id=1460 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=4700 In case of classical continuum mechanics the set of basic equations consists of the equation of motion, the kinematic equation and the constitutive equations. The paper concentrates on the stability problems and the effects of discretization on material modeling. The method of investigation is analytic, the monodromy operator of the discrete system is studied. We study how discretization, stability and anticipation act on one another. As results we show cases, when the anticipatory nature of a material model leads to instability. Mon, 14 Oct 2024 16:36:14 +0200 Mon, 14 Oct 2024 16:36:23 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4700 http://popups.lib.uliege.be/1373-5411/index.php?id=1457 Notions of anticipaton systems for discrete-time and continuous-time lD linear systems and 2D discrete linear systems are introduced. A discrete-time system is called anticipatory if its state vector and output vector depend on the future values of inputs. A continuous-time system is called anticipatory if its state vector and output vector depend on the derivatives of inputs. Necessary and sufficient conditions for the anticipation of singular discrete-time and coutinuous-time l-D linear systems are established. It is shown that the discrete-time system obtained by discretization from continuous-time one is anticipatory for any value of the discretization step if and only if the continuous-time system is anticipatory. Necessary and sufficient conditions for the anticipation of the singular 2D Fornasini - Marchesini model and the singular 2D Roesser model are established. Fri, 12 Jul 2024 14:52:16 +0200 Fri, 12 Jul 2024 14:52:26 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1457