## 5 Simulation Example  
In this section, a simulation example is given to demonstrate the effectiveness of the event-based dual-mode security control strategy under DoS attacks. As shown in Figure 4, we consider a Pulse-Width Modulation (PWM)-driven boost converter borrowed from [44], which can be captured by  
\[ \begin{cases}\dot{E}_{c}(t)=-\dfrac{1}{RC}E_{c}(t)+(1-s(t))\dfrac{1}{C}I_{c}(t)\\ \dot{I}_{c}(t)=-(1-s(t))\dfrac{1}{L}E_{c}(t)+s(t)\dfrac{1}{L}E_{s}(t)\end{cases}  \tag{40}\]  
where \(L\), \(C\) and \(R\) denote the inductance, capacitance and load resistance, respectively. \(E_{c}(t)\) and \(E_{s}(t)\) represent the terminal voltage and source voltage of the capacitor, respectively. \(I_{c}(t)\) is the current through the inductance. \(s(t)\) is a switching signal controlled by a PWM-driven boost converter. Here, as a typical circuit system, the role of using a PWM-driven boost converter is to obtain higher voltage. Let \(x(t)=\text{col}\{E_{c}(t),I_{c}(t),1\}\) be the system state, then the differential Equation (40) is further rewritten as \(\dot{x}(t)=A_{r(t)}x(t)\), \(r(t)\in\{1,2\}\), where the system parameters are \(A_{1}=[-1/RC,1/C,0;-1/L,0,0;0,0,0]\) and \(A_{2}=[-1/RC,0,0;0,0,1/L;0,0,0]\). Selecting \(L=1H\), \(C=1F\), and \(R=1\Omega\), all parameters can be listed as follows: Mode 1:  
\[ \begin{split}& A_{1}=\left[\begin{array}{ccc}-1&1&0\\ -1&0&0\\ 0&0&0\end{array}\right],\,B_{1}^{\omega}=\left[\begin{array}{ccc}0.27&-0.19 &-0.46\\ -0.21&-0.15&0.32\\ 0.55&-0.43&0.17\end{array}\right],\\ & C_{1}=\left[\begin{array}{ccc}-0.11&0.29&0.30\\ 0.05&0.35&0.10\\ -0.10&0.48&0.20\end{array}\right],\,D_{1}^{u}=\left[\begin{array}{c}-0.19\\ 0.15\\ 0.23\end{array}\right].\end{split} \]  
Mode 2:  
\[ \begin{split}& A_{2}=\left[\begin{array}{ccc}-1&0&0\\ 0&0&1\\ 0&0&0\end{array}\right],\,B_{2}^{\omega}=\left[\begin{array}{ccc}0.36&-0.16 &-0.25\\ -0.10&0.35&-0.46\\ 0.32&0.21&-0.19\end{array}\right],\\ & C_{2}=\left[\begin{array}{ccc}-0.20&-0.25&0.32\\ -0.10&0.20&0.34\\ -0.20&0.20&0.35\end{array}\right],\,D_{2}^{u}=\left[\begin{array}{c}0.17\\ -0.21\\ 0.39\end{array}\right],\end{split} \]  
and \(B_{1}^{u}=B_{2}^{u}=\left[ \begin{array}{cc}-0.1&0.4&0.5\end{array} \right]^ {T}\). Without loss of generality, the transition rate matrix is given as  
\[\Pi=\left[ \begin{array}{ccc}-1.2&1.2\\ 0.5&-0.5\end{array} \right],\]  
and the exogenous disturbance signal is assumed to be \(\omega(t)=0.1\sin(x(t))\). According to Theorem 3, the given constants are selected as \(\tau_{p}=0.1\), \(\tau_{q}=0.2\), \(\xi_{1}=0.2\), \(\xi_{2}=0.5\), \(\alpha=0.46\), \(\sigma=0.012\), and \(\gamma=3\). Then, the security controller gains and weighting matrices can be calculated as  
\[ \begin{split}& K_{1}^{a}=\left[\begin{array}{ccc}0.3616&-0.9208 &-0.7812\end{array}\right],\\ & K_{2}^{a}=\left[\begin{array}{ccc}0.1194&-0.7287&-1.3834\end{array}\right],\\ & K_{1}^{b}=\left[\begin{array}{ccc}1.8081&-4.6038&-3.9062\end{array}\right],\\ & K_{2}^{b}=\left[\begin{array}{ccc}0.2387&-1.4573&-2.7667\end{array}\right],\\ &\Theta_{a}=\left[\begin{array}{ccc}0.1133&0.0031&0.0025\\ 0.0031&0.1059&-0.0144\\ 0.0025&-0.0144&0.0904\end{array}\right],\\ &\Theta_{b}=\left[\begin{array}{ccc}1.2865&-0.3221&-0.3076\\ -0.3221&2.2103&1.7366\\ -0.3076&1.7366&4.2373\end{array}\right].\end{split} \]Under the initial state \(x(0)=\left[ \begin{array}{cc}-0.25&0.15&0.24\end{array} \right]^{T}\), Figure 5 presents the state trajectories by using the proposed dual-mode security controller (10) when DoS attacks are not injected over the shared communication network. The time evolution of the regulated output \(z(t)\) and actual state error \(e_{a}(t)\) without DoS attacks are shown in Figure 6 and Figure 7, respectively. Obviously, by using the developed dual-mode security controller (10), the closed-loop MJCPSs (12) achieve stochastic stability and have good robustness. In Figure 8, we show the event-triggered instants determined by the resilient event-triggered condition (8) in the absence of DoS attacks, in which the number of successful transmissions is 67.