From simple to complicated: noncausal bounded input, bounded output stability in linear discrete time models in the deterministic and stochastic cases

AbstractWe consider the question of bounded input, bounded output stability for time-invariant linear systems with a finite dimensional state space and with time axis Z, i.e., all the integers. Our approach also includes the stochastic ARMA models. We do not assume that the inputs are necessarily nonanticipating, and in this respect our results differ from most existing ones. Similar results have been given by Hannan and Deistler and by Brockwell and Davis. Our approach is polynomial-algebra-oriented, and does not use strictly rational functions