of [@hornmatrixanalysis]). On the other hand, for unstable open-loop dynamics, we have $\|A\|>1$. Notice that the inequality in (\[eq:abkcond\]) holds if the upper bound $\overline{v}$ of the average jamming interference power is sufficiently small so that $\hat{p}(\overline{v})$ is sufficiently close to zero. In such cases, transmission failures happen sufficiently rarely in average, and thus the overall networked control system frequently follows the stable behavior of the closed-loop dynamics and the geometric convergence of the first-moment of the state as in (\[eq:moment-convergence\]) can be guaranteed. As we establish in the proof given in the Appendix, the scalar $\overline{\theta}$ in (\[eq:moment-convergence\]) represents the rate of convergence, and it depends on $\hat{p}(\overline{v})$ as well as the scalars $\|A+BK\|$ and $\|A\|$. In particular, if the bound $\overline{v}$ on the long run average jamming interference power is small, then $\overline{\theta}$ is also small, indicating faster convergence of the first-moment.

*First-moment geometric stability* discussed in Proposition \[PropositionMomentConvergence\] is a stronger notion of stochastic stability in comparison to *almost-sure asymptotic stability* explored in [@ahmetifacwc2017]. As expected, first-moment geometric stability condition (\[eq:moment-convergence\]) is more restrictive with respect to the attack parameter $\overline{v}$. Specifically, the almost-sure asymptotic stability condition presented in Theorem 3.5 of [@ahmetifacwc2017] reduces to $$\begin{aligned}
(1-\hat{p}(\overline{v}))\ln\|A+BK\|+\hat{p}(\overline{v})\ln\|A\| 