## 4 Numerical Simulations
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & **CC1** & **CC2** & **CC3** & **CC4** & **CC5** & **CC6** & **Uncontrolled** \\ \hline Building \(\mathcal{B}^{(1)}\) (4 th story) & 7.5438 & 6.7569 & 7.8870 & 5.7426 & – & 5.9200 & 9.5253 \\ Building \(\mathcal{B}^{(2)}\) (5 th story) & 6.7197 & 8.4009 & 5.4798 & 7.6020 & – & 6.8801 & 9.6258 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Passive controllers. Absolute acceleration peak-values (m/s\({}^{2}\)) of the buildings’ top-level stories corresponding to the uncontrolled response and the passive velocity-feedback controllers defined by the gain matrices \(\widetilde{\mathbf{K}}^{\ell}\). The values of the control configuration CC5 are missing due to the feasibility issues encountered in the associated LMI optimization problem. Figure 15: _Story absolute acceleration peak-values for the control configurations CC3 and CC4._ Maximum story absolute acceleration corresponding to the uncontrolled configuration (black solid line with squares), the active controller defined by the control gain matrix \(\mathbf{K}^{\text{int}}\) (blue solid line with circles), the passive controller defined by the control gain matrix \(\widetilde{\mathbf{K}}^{\text{int}}\) (blue dashed line with asterisks), the active controller defined by the control gain matrix \(\mathbf{K}^{\text{tr}}\) (red solid line with triangles) and the passive controller defined by the control gain matrix \(\widetilde{\mathbf{K}}^{\text{tr}}\) (red dotted line with hexagrams). \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & **CC1** & **CC2** & **CC3** & **CC4** & **CC5** & **CC6** & **Uncontrolled** \\ \hline Building \(\mathcal{B}^{(1)}\) (4 th story) & 7.5070 & 6.4787 & 7.3414 & 5.7286 & 6.0715 & 4.7087 & 9.5253 \\ Building \(\mathcal{B}^{(2)}\) (5 th story) & 5.9233 & 9.0380 & 5.2443 & 7.2716 & 6.1648 & 7.3445 & 9.6258 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Active controllers. Absolute acceleration peak-values (m/s\({}^{2}\)) of the buildings’ top-level stories corresponding to the uncontrolled response and the active velocity-feedback controllers defined by the gain matrices \(\mathbf{K}^{\ell}\). of the linked control configuration CC6 while, in contrast, an interbuilding separation of 5 cm would produce interbuilding collisions for the active controller of the unlinked control configuration CC5. For the uncontrolled configuration, a interbuilding gap of more than 25 cm would have been necessary to avoid rounding events._  
**Remark 3**. : _It should be noted that the linked control configuration CC2 is an incomplete actuation scheme, in the sense that it does not include any interstory actuation device in building \(\mathcal{B}^{(1)}\). This element can possibly help to explain its reduced effectiveness in mitigating the interstory drift response. In contrast, all the other control configurations include a more balanced actuation scheme with interstory actuation devices in both buildings._  
**Remark 4**. : _Although no general conclusions can be drawn from the considered particular configurations, the obtained numerical results seem to indicate that the presence of interbuilding actuation devices can produce opposite effects in the acceleration response of linked buildings with a different height. This fact certainly opens a number of interesting questions related to the acceleration response characteristics of linked buildings, such as the relevance of the height difference, the behavior of linked buildings with the same height, and the effect of multiple linking devices._