## 4 Results and Discussion  
### Event-Triggered Collaborative Switching of Multi-Microwave Agents under DoS Attacks  
This article uses six microwave sources symmetrically distributed pairwise. Assuming node 0 is the leader, and 1 to 5 denote followers. The adjacency matrix \(\mathcal{A}\) for followers and the adjacency matrix \(\mathcal{B}\) for leaders can be obtained from Figure 4.  
The initial parameter settings are as follows:  
\[\mathrm{A}=\left[ \begin{array}{cccc}0&0&0&1&0\\ 0&0&1&1&0\\ 0&1&0&0&1\\ 1&1&0&0&0\\ 0&0&1&0&0\\ \end{array} \right],B=\left[ \begin{array}{c}4\\ 1\\ 1\\ 0\\ 1\\ \end{array} \right],\mathrm{P}_{i}(0)=\left[ \begin{array}{c}4\\ 2\\ 4\\ 1\\ 2\\ \end{array} \right]\]  
As described in Section 3, let \(\mathrm{P}_{0}(0)=1\), \(\chi=0.9\), \(\vartheta=8.2\) calculating \(\bar{p}\), \(\delta_{\min}\), \(\Gamma\)and \(\tau_{\min}\) using the LMI Toolbox in Matlab (version number: 9.13.0.2049777 (R2022b)) as follows:  
\[\bar{p}=\left[ \begin{array}{cccc}0.0923&0.0011&0.0001&0.0103&0.0000\\ 0.0011&0.0935&0.0104&0.0104&0.0011\\ 0.0001&0.0104&0.0934&0.0012&0.0103\\ 0.0103&0.0104&0.0012&0.0934&0.0001\\ 0.0000&0.0011&0.0103&0.0001&0.0923\\ \Gamma=\left[0.3703&0.0992&0.0212&0.0518&0.0935\right]\\ \end{array} \right]\]  
And the \(\delta_{\min}=0.5188\), take \(\delta_{\min}=0.5\) to satisfy \(0<\delta_{m1}<\delta_{\min}\), we can obtain \(\tau_{\min}\geq 0.0011\) s from Equations (12)-(14). Inspired by [26,28], let \(q_{i_{1}j_{1}}\in[0.1,0.2]\), \(\left|q_{i_{1}i_{1}}\right|\in[0.1,0.2]\). The proposed method only requires knowledge of the maximum values of \(\bar{q}\) and \(\bar{q}\) in Equation (20), as accurately measuring the transition rate during switching is difficult. So, \(\tau_{\min}<\min\{q_{i_{1}j_{1}},\left|q_{i_{1}i_{1}}\right|\}\); therefore, in the experiment \(\tau_{\min}=0.01\) s. The leader switching trajectory is as follows:  
\[f\left(t,\dot{\mathrm{P}}_{0}(t)\right)=5 square(\psi\times t\times pi,50 sawtooth (\zeta\times t\times pi))-\alpha\mathrm{P}_{0}(t)\]  
Let \(\psi=0.2\), \(\zeta=0.8\), \(\omega=100\), \(\eta=2.8\), \(\beta=\sqrt{\chi(\delta_{1}-\frac{k_{2}}{\theta})/(k_{1}+k_{2}\theta)}=0.22\). The time for DoS attacks is set to \(T_{n}^{off}-T_{n}^{on}=0.05\) s, followed by \(T_{n+1}^{on}-T_{n}^{off}=0.15\) s of silence, and the cycle repeats every \(T=T_{n+1}^{on}-T_{n}^{on}=0.2\) s, and assuming the system experiences  
Figure 4: Fixed communication topology of multi-source microwave intelligent agents. the DoS attacks \(T_{Dos}\in(20,30)\) s. When \(q_{i_{1}j_{1}}\in[0.1,0.2]\), \(\left|q_{i_{1}i_{1}}\right|\in[0.1,0.2]\), there is a value of \(\mu\geq 1\), and \(\lambda>\lambda_{1}>0\), make the \(\mu q-\bar{q}\leq(\lambda(T-\bar{T})+\lambda_{1}\bar{T})/T\) satisfies the inequality. During the no DoS attacks, the result of Equations (6) and (8) is shown in Figure 5a. The event-triggered frequency can be obtained from Equation (9), as shown in Figure 6.  
During the DoS attacks, the system state switching under the DoS attacks is shown in Figure 5b using the control law Equation (11) and event-triggered strategy Equation (8). Additionally, Figure 7 shows the time distribution of event-triggered for intelligent agents during the DoS attacks. When \(t=T_{Dos}\in(20,30)\) s, the DoS attack takes effect, and the error of the intelligent agent in the switching system increases, as shown in the comparison between Figure 5a,b, which leads to a rise in the number of event- triggered for the intelligent agent, illustrated in Figures 6 and 7. While \(t>30\) s, there is no DoS attack, and the switching system can maintain stability. As indicated in Table 3, for \(t=T_{DoS}\in(20,30)\) s, due to the existence of DOS attacks, there was an increase of 24, 15, 22, 18, and 10 in the number of event-triggered occurrences for agents 1-5, respectively. Noticeably, the frequency of event-triggered increases and the performance of system switching decreases when the system considers DoS attacks, as shown by comparing Figure 5a,b.