that $$\begin{aligned}
\mathbb{P}\big[\sum_{i=0}^{t-1}v(i)\leq\overline{\kappa}+\overline{v}t\big] & =1,\quad t\in\mathbb{N}.\label{eq:attack_assumption_one}\end{aligned}$$

Here, $\overline{v}\geq0$ is an asymptotic upper-bound on the average interference power (i.e., $\limsup_{k\to\infty}\frac{1}{k}\sum_{t=0}^{k-1}v(t)\leq\overline{v}$). Notice that if $p$ in (\[eq:ldef\]) is a concave function, then $p(\overline{v})$ can be used in the stability analysis as an upper bound on the long run average number of transmission failures. On the other hand, if $p$ is not concave, then a concave function that upper-bounds $p$ can be used for the same purpose. To this end, we utilized in [@ahmetifacwc2017] a continuous, nondecreasing, and concave function $\hat{p}\colon[0,\infty)\to[0,1]$ such that $$\begin{aligned}
\hat{p}(v) & \geq p(v),\quad v\in[0,\infty).\label{eq:p_phat_ineq}\end{aligned}$$ As discussed in [@ahmetifacwc2017], such a $\hat{p}$ always exists, and moreover, $$\begin{aligned}
\limsup_{t\to\infty}\frac{1}{t}\sum_{i=0}^{t-1}l(i) & \leq\hat{p}(\overline{v}),\label{eq:long-run-bound}\end{aligned}$$ almost surely. In other words, the average number of transmission failures is upper bounded in the long run by $\hat{p}(\overline{v})$. The inequality (\[eq:long-run-bound\]) was used in [@ahmetifacwc2017] for establishing stability of the closed-loop system (\[eq:closed-loop-system\]) in the case without disturbance. The analysis in [@ahmetifacwc2017] indicates that if $\overline{v}$ is sufficiently small, then the closed-loop system is asymptotically stable almost surely, implying $\mathbb{P}[\lim_{t\to\infty}\|x(t)\|_{2}=0]=1$.

In addition, moment stability of the networked control system can also be analyzed under Assumption \[FirstAssumption\]. In particular, the following result provides a condition under which the 