## Appendix A Proof of the Theorem 2
\begin{split}\frac{d\|e_{a}(t)\|}{\text{dt}}&\leq \Big{\|}A_{r(t_{k})}e_{a}(t)+A_{r(t_{k})}x(t_{k})\\ &\quad+B_{r(t_{k})}^{\omega}\omega(t)+\hat{B}_{r(t_{k})}^{u}x(t_ {n}^{\ell})\Big{\|},\end{split} \] (101)  
where \(\hat{B}_{r(t_{k})}^{u}=\xi_{r(t_{k})}B_{r(t_{k})}^{u}K_{r(t_{k})}^{b}\). Then, it follows from (101) that \(\frac{d\|e_{a}(t)\|}{\text{dt}}\leq\theta_{1}(\|e_{a}(t)\|+\|x(t_{k})\|)+ \theta_{3}\|\omega(t)\|+\theta_{4}\|x(t_{n}^{\ell})\|\), where \(\theta_{4}\) is given in Theorem 2. Similarly, we define a virtual intermediate variable \(g(t)\) satisfying \(g(t)=\theta_{1}(g(t)+\|x(t_{k})\|)+\theta_{3}\|\omega(t)\|+\theta_{4}\|x(t_{n }^{\ell})\|\), whose solution can be calculated as  
\[ \begin{split} g(t)&=\frac{\Big{[}\theta_{1}\|x(t_ {k})\|+\theta_{3}\|\omega(t)\|+\theta_{4}\|x(t_{n}^{\ell})\|\Big{]}}{\theta_{1} }\\ &\quad\times\Big{(}e^{\theta_{1}(t-t_{k})}-1\Big{)}.\end{split}  \tag{102}\]  
Substituting \(\|x(t_{k})\|\leq\|e_{a}(t)\|+\|x(t)\|\) into (102), we obtain \(\|e_{a}(t)\|\leq\theta_{1}^{-1}[\theta_{1}\|e_{a}(t)\|+\theta_{1}\|x(t)\|+ \theta_{3}\|\omega(t)\|+\theta_{4}\|x(t_{n}^{\ell})\|]\times(e^{\theta_{1}(t- t_{k})}-1)\). Meanwhile, it can be known from the resilient event-triggered rule (8) that \(q_{1}^{2}\|e_{a}(t)\|^{2}\leq\sigma_{0}^{2}\|x(t)\|^{2}+\hat{\omega}^{2}\mathcal{J }_{d}+\sigma^{2}\|\omega(t)\|^{2}+\hat{\omega}^{2}\|x(t_{n}^{\ell})\|^{2}\) is established when there are DoS attacks, where \(\hat{\omega}\) and \(\hat{\omega}\in\mathbb{R}_{>0}\) are given scalars. Subsequently, we need to focus on the relationship between \(\|e_{a}(t)\|\), \(\|x(t_{n}^{\ell})\|\), \(\|x(t)\|\), \(\|x(t)\|\), \(\|\omega(t)\|\), and \(\mathcal{J}_{d}\). Based on [PERSON]'s inequality, it can be concluded that \(\|e_{a}(t)\|\leq\varsigma_{3}\|x(t)\|+\varsigma_{4}\|\omega(t)\|+\varsigma_{5 }\|x(t_{n}^{\ell})\|+\varsigma_{6}\tilde{\mathcal{J}}_{d}\), where \(\tilde{\mathcal{J}}_{d}=\sqrt{\mathcal{J}_{d}}\), \(\varsigma_{3}\), \(\varsigma_{4}\), \(\varsigma_{5}\), and \(\varsigma_{6}\in\mathbb{R}_{>0}\) are defined in Theorem 2. From this, one can yield  
\[\frac{1}{\theta_{1}}\text{In}\bigg{[}\frac{\text{Y}_{1}(x(t),\omega(t),x(t_{n }^{\ell}),\tilde{\mathcal{J}}_{d})}{\text{Y}_{2}(x(t),\omega(t),x(t_{n}^{\ell} ),\tilde{\mathcal{J}}_{d})}+1\bigg{]}\leq\Delta_{k}, \tag{103}\]  
where \(\text{Y}_{1}(x(t),\omega(t),x(t_{n}^{\ell}),\tilde{\mathcal{J}}_{d})=\theta_{ 15}\lambda[x(t)\|+\theta_{154}\|\omega(t)\|+\theta_{155}\|x(t_{n}^{\ell})\|+ \theta_{16}\varsigma_{6}\tilde{\mathcal{J}}_{d}\) and \(\text{Y}_{2}(x(t),\omega(t),x(t_{n}^{\ell}),\tilde{\mathcal{J}}_{d})=\theta_{ 1}(\varsigma_{3}+1)\|x(t)\|+(\theta_{15}\varsigma_{4}+\theta_{3})\|\omega(t)\|+ (\theta_{155}+\theta_{4})\|x(t_{n}^{\ell})\|+\theta_{16}\varsigma_{\tilde{ \mathcal{J}}_{d}}\). This implies that the inter-execution interval \(\Delta_{k}\) is greater than or equal to \(\Delta_{\text{min}}^{2}\) defined in condition (29). **Case II**: Some jumps occur during the interval \([t_{k},t_{k+1})\). This means that \(t_{\bar{k}}\leq t_{k}<t_{\bar{k}+1}<\cdots<t_{\bar{k}+l}\leq t_{k+1}\) with \(l\in\mathbb{S}\). Once there are some jumps during the interval \([t_{k},t_{k+1})\), we need to divide it into a group of subintervals based on the jump instants. Furthermore, it can be seen from the above derivation that conditions (101) and (101) are satisfied regardless of whether DoS attacks are dormant or active. Since the jump signal \(r(t_{\bar{k}})\), \(\bar{k}\in\mathbb{N}_{0}\) obeys a right-continuous Markov process, this indicates that either \(\|e_{a}(t_{\bar{k}+1}^{-})\|\leq f(t_{\bar{k}+1}^{-})\) or \(\|e_{a}(t_{\bar{k}+1}^{-})\|\leq g(t_{\bar{k}+1}^{-})\) can be satisfied for the first subinterval \([t_{\bar{k}},t_{\bar{k}+1})\). Notice that \(x(t_{k})\) is maintained within the transmission interval \([t_{k},t_{k+1})\) due to the effect of ZOH.