## Appendix A Proof of the Theorem 2
In this case, no matter the subinterval, we can obtain \(\|e_{a}(t_{\bar{k}+h}^{-})\|=\|e_{a}(t_{\bar{k}+h})\|\leq f(t_{\bar{k}+h})=f(t_{ \bar{k}+h}^{-})\) and \(\|e_{a}(t_{\bar{k}+h}^{-})\|=\|e_{a}(t_{\bar{k}+h}^{-})\|\leq g(t_{\bar{k}+h}^{-})\). Thus, the same conclusion can be drawn as in Case I. That is, conditions (101) and (101) always hold, where there exist some jumps during the transmission interval \([t_{k},t_{k+1})\). In summary, the parameter \(\Delta_{\text{min}}\) determined by (101) and (101) is regarded as the minimum execution interval, implying that Zeno behavior can be avoided. On the other hand, DoS attacks can cause a severe mismatch of information between S-C and C-A sides. Therefore, we need to calculate the maximum downtime, which is reflected by the maximum update interval between two successful transmission attempts subject to the resilient event-triggered rule (8). Firstly, before embarking on this study, it can be concluded from Case I and Case II that the presence or absence of jumps during each transmission interval has no effect on estimating \(\|e_{a}(t)\|\). Next, if \(-e_{a}^{T}(t)\Theta_{a}e_{a}(t)+\sigma x^{T}(t)\Theta_{b}x(t)+\sigma^{2}\| \omega(t)\|^{2}+\tilde{\sigma}^{2}\|x(t_{n}^{\ell})\|^{2}+\tilde{\sigma}^{2} \mathcal{J}_{d}>0\) is satisfied, then we can derive \(\|e_{a}(t)\|\leq\xi_{3}\|x(t)\|+\xi_{4}\|\omega(t)\|+\xi_{5}\|x(t_{n}^{\ell})\| +\xi_{6}\mathcal{J}_{d}\), where \(\mathcal{J}_{d}\) is given in (A8) and the parameters \(\xi_{3}\), \(\xi_{4}\), \(\xi_{5}\), \(\xi_{6}\) are defined in Theorem 2. In view of the accumulation of sampling errors caused by DoS attacks, a large number of packets from S-C side cannot be transmitted normally. Therefore, it is necessary to re-estimate \(\|e_{a}(t)\|\) over time period \([\mathcal{T}_{n},\mathcal{T}_{n+1})\), \(n\in\mathbb{N}_{0}\). Intuitively, we need to discuss the internal relationship between the latest transmission instant and DoS initiation instant. From this, the estimation of \(\|e_{a}(t)\|\) during \([\mathcal{T}_{n},\mathcal{T}_{n+1})\) can be divided into the following three steps. **Step I**: The latest transmission attempt occurs at \(\mathcal{T}_{n}^{\text{on}}\), that is, \(t_{k}:=\mathcal{T}_{n}^{\text{on}}\), where \(t_{k}\) and \(\mathcal{T}_{n}^{\text{on}}\) denote the latest transmission and DoS initiation instants, respectively. Then, we obtain that  
\[\|e_{a}(t)\| \leq\xi_{3}\|x(t)\|+\xi_{3}(1+\xi_{3})\|x(t)\|+\xi_{4}(2+\xi_{3})\] (A9) \[\times\|\omega(t)\|+\xi_{5}(2+\xi_{3})\|x(t_{n}^{\ell})\|+\xi_{6} (2+\xi_{3})\mathcal{J}_{d},\]  
where \(t\in[t_{n}^{\ell},t_{n}^{\ell+1})\). Since there may be some abnormal event-triggered packets during \([\mathcal{T}_{n}^{\text{on}},\mathcal{T}_{n+1})\), it follows from (A9) that  
\[\|e_{a}(t)\| \leq\xi_{3}[1+\xi_{3}+2\xi_{3}+\cdots+2^{N_{\text{doS}}}\xi_{3}] \|x(t)\|\] (A10) \[\quad+\xi_{4}[1+\xi_{3}+2\xi_{3}+\cdots+2^{N_{\text{doS}}}\xi_{3}] \|\omega(t)\|\] \[\quad+\xi_{5}[1+\xi_{3}+2\xi_{3}+\cdots+2^{N_{\text{doS}}}\xi_{3}] \|x(t_{n}^{\ell})\|\] \[\quad+\xi_{6}[1+\xi_{3}+2\xi_{3}+\cdots+2^{N_{\text{doS}}}\xi_{3}] \mathcal{J}_{d}\] \[=\left[\xi_{3}\|x(t)\|+\xi_{4}\|\omega(t)\|+\xi_{5}\|x(t_{n}^{\ell })\|+\xi_{6}\mathcal{J}_{d}\right]\] \[\quad\times\left[1+\sum_{n_{f}=1}^{N_{\text{doS}}+1}2^{n_{f}-1} \xi_{3}\right],\]  
where \(\xi_{3}=\xi_{3}+1\), and \(N_{\text{doS}}\) is the maximum number of packet losses caused by DoS attacks during \([\mathcal{T}_{n}^{\text{on}},\mathcal{T}_{n+1})\). **Step II**: The latest transmission attempt occurs before \(\mathcal{T}_{n}^{\text{on}}\), that is, \(t_{k}<\mathcal{T}_{n}^{\text{on}}\) is established.