# Protocol for Energy-Efficiency in Networked Control Systems Based on WSN
## 6 Example of Application of the Energy-Efficiency Protocol
### Results
#### 6.3.3 Energy Saving Protocol--Third Method: Mixed Problem
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \(I_{L_{m}}\) & \(U\) & \(\mathbf{Pr}(\bar{g}_{1})\) & \(\mathbf{Pr}(\bar{g}_{2})\) & \(\mathbf{Pr}(\bar{n}_{1})\) & \(\mathbf{Pr}(\bar{n}_{2})\) \\ \hline
1 & \(-\) & 0.9768 & 0.9845 & 0.9588 & 0.9188 \\
2 & 13 & 0.9768 & 0.9845 & 0.9588 & 0.8618 \\
3 & 9 & 0.9768 & 0.9845 & 0.9183 & 0.8618 \\
4 & 14 & 0.9768 & 0.9845 & 0.9183 & 0.8084 \\
5 & 10 & 0.9768 & 0.9845 & 0.8794 & 0.8084 \\
6 & 15 & 0.9768 & 0.9845 & 0.8794 & 0.7583 \\
7 & 11 & 0.9768 & 0.9845 & 0.8422 & 0.7583 \\
8 & 1 & 0.9500 & 0.9845 & 0.8422 & 0.7583 \\
9 & 6 & 0.9500 & 0.9574 & 0.8422 & 0.7583 \\
10 & 16 & 0.9500 & 0.9574 & 0.8422 & 0.7112 \\
11 & 12 & 0.9500 & 0.9574 & 0.8066 & 0.7112 \\
12 & 2 & 0.9239 & 0.9574 & 0.8066 & 0.7112 \\
13 & 3 & 0.8985 & 0.9574 & 0.8066 & 0.7112 \\
14 & 4 & 0.8739 & 0.9574 & 0.8066 & 0.7112 \\
15 & 7 & 0.8739 & 0.9312 & 0.8066 & 0.7112 \\
16 & 5 & 0.8499 & 0.9312 & 0.8066 & 0.7112 \\
17 & 8 & 0.8499 & 0.9056 & 0.8066 & 0.7112 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Probabilities of successful transmission for each new setting of the network such that the nodes \(U\) exchange \(L\in\{8,5\}\) following the sequence \(I_{Lm}\) (Mixed approach). Figure 7: Performance measurement index \(\Theta\) in terms of a fixed \(L\) for the network under investigation. where \(\mathcal{H}_{\infty}^{A2}(I_{L_{m}})\) and \(\mathcal{H}_{\infty}^{A3}(I_{L_{m}})\) respectively represent the \(\mathcal{H}_{\infty}\) norm of the closed-loop system computed by the second approach (energy by node approach) and the third approach (mixed approach) for each network setting indexed by \(I_{L_{m}}\). On the other hand, Figure 8c shows that the global energy consumption \(E_{GE}\) decreases monotonically with the augmentation of the number of devices operating in the energy saving work mode. Analogously to what was done for the \(\mathcal{H}_{\infty}\) norm, Figure 8b illustrates the percentage augmentation of \(E_{GE}\) for each network setting when compared with the value obtained by the second method:  
\[E_{GE}\%=\frac{E_{GE}^{A3}(I_{L_{m}})-E_{GE}^{A2}(I_{L_{m}})}{E_{GE}^{A2}(I_{ L_{m}})}\times 100,\]  
where \(E_{GE}^{A2}(I_{L_{m}})\) and \(E_{GE}^{A3}(I_{L_{m}})\) respectively represent the global energy consumption associated with the second approach (energy by node approach) and with the third approach (mixed approach) for each network setting indexed by \(I_{L_{m}}\). Figure 8: (**a**) \(\mathcal{H}_{\infty}\) norm of the closed-loop system using the mixed approach; (**b**) Percentage difference between the norm obtained by the second and third energy saving protocols; (**c**) The global energy consumption (\(E_{GE}\)) of the network using the mixed approach; (**d**) Percentage difference between the global energy consumptions obtained by the second and third energy saving protocols. All the parameters are evaluated in terms of the distinct network settings organized according to the sequence \(I_{Lm}\).