This paper studies the expectationally boundedness of stable linear time invariant (LTI) systems in the presence of nonvanishing stochastic perturbations. First, expectationally bounded random processes are defined and their characteristics are investigated. Afterward a theorem is stated, which assigns an upper bound to the Euclidean norm of the states of an intrinsically LTI stable system in the case that it is perturbed by nonvanishing stochastic perturbations.

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