(\[eq:expectation\_bounded\_noise\_case\]). $\blacksquare$

\[RemarkFirstHatValues\] By using (\[eq:thetamudhat\]) together with (\[eq:ThetaDef\]), (\[eq:MuDef\]), and (\[eq:DDef\]), we can obtain the values of $\hat{\theta}$, $\hat{\mu}$, and $\hat{d}$ as $$\begin{aligned}
 & \hat{\theta}=(1-\hat{p}(\frac{\hat{\kappa}}{T^{*}}+\hat{v}))\|A+BK\|+\hat{p}(\frac{\hat{\kappa}}{T^{*}}+\hat{v})\|A\|,\label{eq:ThetaHatValue}\\
 & \hat{\mu}=\frac{c_{2}}{c_{1}}\|A\|{}^{T^{*}-1}\hat{\theta}^{-(T^{*}-1)},\label{eq:MuHatValue}\\
 & \hat{d}=\frac{c_{2}}{c_{1}}\Big(\frac{\|A\|{}^{T^{*}-1}\hat{\theta}^{-(T^{*}-1)}}{1-\hat{\theta}}+1\Big),\label{eq:DHatValue}\end{aligned}$$ where $T^{*}$ is a positive integer that satisfies $$\begin{aligned}
 & (1-\hat{p}(\frac{\hat{\kappa}}{T^{*}}+\hat{v}))\|A+BK\|+\hat{p}(\frac{\hat{\kappa}}{T^{*}}+\hat{v})\|A\|<1,\end{aligned}$$ and $c_{1},c_{2}>0$ are scalars that satisfy (\[eq:norm-equivalence\]). The attacker with large resources can cause the state norm to grow large. This is also indicated in the upper bound for the first moment given in (\[eq:noise\_to\_state\_one\]). In particular, if $\hat{\kappa}$ in Assumption \[SecondAssumption\] is large, then $T^{*}$ is large, which makes $\hat{\mu}$ large, as $\hat{\mu}$ is an increasing function of $T^{*}$. Further, since $$\begin{aligned}
 & \frac{c_{2}}{c_{1}}\Big(\frac{\hat{\mu}}{1-(1-\hat{p}(\hat{v}))\|A+BK\|-\hat{p}(\hat{v})\|A\|}+1\Big)\leq\hat{d},\end{aligned}$$ we observe that $\hat{d}$ is large for large values of $\hat{\mu}$ and $\hat{v}$. On the other hand, for large values of $T^{*}$, $\hat{\theta}$ is close to $(1-\hat{p}(\hat{v}))\|A+BK\|+\hat{p}(\hat{v})\|A\|$. If the upper bound $\hat{v}$ of average interference powers is large, then $\hat{\mu}\hat{\theta}^{t}$ in (\[eq:noise\_to\_state\_one\]) converges slowly, since $\hat{\theta}$ is close to $1$.

Jamming and Disturbance with Finite Second Moment {#subsec:Stabilization-Under-Jamming}
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In Theorem \[TheoremBoundedDisturbance\], we explored the case where the disturbance norm is bounded at each time almost surely. Next, we investigate scenarios where the disturbance may not be bounded. We obtain a relation between the 