  In this paper we prove the time-domain boundedness for noise-to-state
exponentially stable systems, and further make an estimation of its lower bound
function, which allows to answer the question that how long the solution of a
stochastic noise-to-state exponentially stable system stays in the domain of
attraction and what happens with it if it escapes from this region for a while.
The results will complement the probability-domain boundedness of
noise-to-state exponentially stable systems, and provide a new insight into
noise-to-state exponential stability.
