Abstract
Abstract This paper studies stochastic boundedness of trajectories of a non-vanishing stochastically perturbed stable linear time-invariant system. First, two definitions on stochastic boundedness are presented, then, the boundedness is analyzed via Lyapunov theory. A theorem is proposed, which shows that under a condition on the Lipchitz constant of the perturbation kernel, the trajectories remain stochastically bounded, and the bounds are calculated. Also, the limiting behaviour of the trajectories is studied. At the end, an illustrative example is presented, which shows the effectiveness of the proposed theory.
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