## 5 Numerical Example  
In this section, the effectiveness of the proposed method will be verified based on simulation examples. As coal progresses through various stages from raw to finished product, each storage phase is influenced by factors such as natural weathering, rain, and snow erosion, leading to varying storage loss rates. Considering the operational data of a coal enterprise [35],the model parameters are set as follows according to the actual situation and the historical data of the enterprise: the inventory loss rate is \(\text{diag}\left[0.08\quad 0.05\quad 0.03\quad 0.02\right]\). The upper bounds of the interaction delay are given as \(\overline{\tau_{1}}=4\) and \(\overline{\tau_{2}}=7\). The initial stock values for the three subchains are: \(x_{i}(0)=\left[90\quad 60\quad 70\quad 40\right]^{T}\) tons, \(x_{j}(0)=\left[50\quad 40\quad 60\quad 90\right]^{T}\) tons, and \(x_{m}(0)=\left[70\quad 50\quad 70\quad 60\right]^{T}\) tons. The control targets for inventory are \(\left[15\quad 19\quad 22\quad 25\right]\). The control objective is to ensure uninterrupted logistics and to manage inventory levels such that higher loss rates result in lower steady-state inventory. This approach aims to effectively reduce the economic losses associated with inventory loss rates. The parameters \(\alpha=0.7\), \(\alpha^{*}=0.45\), and \(\beta=0.53\) are used in the model. The system's topology is forced to change when a significant accidental event occurs, causing breaks in the supply chain nodes and resulting in isolated nodes. The switching of the system topology is illustrated in Figure 2. During normal operations, the trust value between subchains increases with the number of successful transactions. However, the emergence of isolated nodes impacts the trustworthiness of each subchain to varying extents. The switching signals generated by the system due to isolated nodes are depicted in Figure 3, where the \(y\)-axis coordinates 1, 2, and 3 correspond to the presence of isolated nodes in subchains i, j, and m, respectively, and the corresponding changes in the trustworthiness of the subchains are shown in Figure 4. The controller gains are shown below. Figure 3: Switching signals. Figure 2: Topology switching (Red indicates isolated nodes). \[\widetilde{K_{0}}= \begin{bmatrix}-0.0418&-0.0492&-0.0539&-0.0572\\ -0.0317&-0.0368&-0.0403&-0.0428\\ -0.0211&-0.0248&-0.0268&-0.0284\\ -0.0106&-0.0124&-0.0136&-0.0140\\ \end{bmatrix} \widetilde{K_{0}}= \begin{bmatrix}0.0265&0.0312&0.0342&0.0362\\ 0.0202&0.0234&0.0256&0.0271\\ 0.0134&0.0157&0.0170&0.0180\\ 0.0067&0.0079&0.0086&0.0089\\ \end{bmatrix} \]  
\[\widetilde{K_{\
u}}= \begin{bmatrix}-0.0424&-0.0472&-0.0501&-0.0522\\ -0.0289&-0.0363&-0.0386&-0.0401\\ -0.0193&-0.0217&-0.0270&-0.0280\\ -0.0096&-0.0108&-0.0116&-0.0159\\ \end{bmatrix} \widetilde{K_{\
u}}= \begin{bmatrix}0.0484&-0.0942&-0.1002&-0.1043 \\ -0.0656&-0.0699&-0.0744&-0.0775\\ -0.0437&-0.0486&-0.0486&-0.0507\\ -0.0219&-0.0243&-0.0258&-0.0239\\ \end{bmatrix} \]  
Based on the conditions described above, the changes in the inventory status of each node in the supply chain can be observed in Figure 5. In this figure, parts (a) and (b) represent the inventory changes at the head and tail nodes of the supply chain, which are most affected by perturbations. Part (c) illustrates the inventory changes of the ith sub-chain. Finally, part (d) displays the inventory error variation curves for all sub-chains. Figure 4: Trust change. Figure 5: Inventory changes: (**a**) inventory changes at the supplier nodes of subchains i, j, m; (**b**) inventory changes at the retailer nodes of subchains i, j, m; (**c**) inventory changes at the four nodes of subchain i; and (**d**) changes in consistency error among all nodes. From Figure 5, it is evident that the inventory levels of all facilities within the supply chain system converge to a uniform level. This prevents scenarios of stockouts in some regions and excess inventory in others due to uneven distribution, thereby enhancing the overall efficiency of the supply chain.