Stochastic stability of coupled linear systems: a survey of methods and results

The analysis of dynamic systems subject to stochastic parametric excitation is important in a variety of branches of engineering and physics. For example, models of this type frequently occur in the analysis of linear continuous systems using modal decomposition. The random coupling or parametric excitation can, for example, model the influence of externally applied loads on the system parameters. In this paper we investigate the almost–sure stability properties of the sample trajectories of linear stochastic systems with parametric excitation.