\[SecondAssumption\] with a sufficiently small $\hat{v}$ such that (\[eq:abkcond-vhat\]) holds, then the first moment of the state stays bounded. Furthermore, the upper bound given in (\[eq:noise\_to\_state\_one\]) is geometrically decreasing towards the constant $\hat{d}\overline{w}$, where $\overline{w}$ is an upper bound on the Euclidean norm of disturbance $w(t)$. Notice that the condition (\[eq:abkcond-vhat\]) of Theorem \[TheoremBoundedDisturbance\] and the condition (\[eq:abkcond\]) in the disturbance-free case in Proposition \[PropositionMomentConvergence\] are in the same form, but use different scalars $\hat{v}$ and $\overline{v}$ due to the difference of the jamming interference characterizations in Assumptions \[FirstAssumption\] and \[SecondAssumption\]. We remark that for attacks that satisfy both assumptions, we have $\overline{v}\leq\hat{v}$.

As we establish in the proof of Theorem \[TheoremBoundedDisturbance\], the first moment upper bound in (\[eq:noise\_to\_state\_one\]) depends on attack parameters $\hat{\kappa}$ and $\hat{v}$. In particular, the values of $\hat{\mu}$ and $\hat{d}$ are large, if $\hat{k}$ and $\hat{v}$ take large values. Moreover, the scalar $\hat{\theta}$ is directly related to the term $(1-\hat{p}(\hat{v}))\|A+BK\|+\hat{p}(\hat{v})\|A\|$ on the left-hand side of (\[eq:abkcond-vhat\]). If this term is close to zero, then $\hat{\theta}$ is close to zero, which indicates faster convergence of the bound in (\[eq:noise\_to\_state\_one\]) towards the constant $\hat{d}\overline{w}$. We note that $(1-\hat{p}(\hat{v}))\|A+BK\|+\hat{p}(\hat{v})\|A\|$ represents the behavior of the overall networked control system and 