## 4 Numerical Simulations
Additionally, to provide a wider vision of the acceleration response characteristics, the story absolute acceleration peak-values corresponding to the uncontrolled configuration and the active and passive controllers proposed for the control configurations CC3 and CC4 are displayed in Figure 15. Looking at the values of building \(\mathcal{B}^{(1)}\) in Table 5, it can be appreciated that better results are attained by the linked control configurations. In this case, the best performance is achieved by the linked configuration CC6, which produces a 50.6% of reduction with respect to the uncontrolled response. In contrast, the values of building \(\mathcal{B}^{(2)}\) indicate a better behavior of the unlinked control configurations. For this building, the best performance corresponds to the unlinked control configuration CC3, which produces a 45.5% of reduction with respect to the uncontrolled response. Looking at the data in Table 6, a similar pattern can be appreciated in the values produced by the passive controllers. In this case, the best results are attained by the linked configuration CC4 in  
Figure 14: _Interstory drift and interbuilding approach peak-values for the control configurations CC5 and CC6._ Maximum absolute interstory drifts and maximum interbuilding approaches corresponding to the uncontrolled configuration (black solid line with squares), the active controller defined by the control gain matrix \(\mathbf{K}^{\mathrm{v}}\) (blue solid line with circles), the active controller defined by the control gain matrix \(\mathbf{K}^{\mathrm{v}}\) (red solid line with triangles) and the passive controller defined by the control gain matrix \(\mathbf{\hat{K}}^{\mathrm{v}}\) (red dotted line with hexagrams). Figure 13: _Interstory drift and interbuilding approach peak-values for the control configurations CC3 and CC4._ Maximum absolute interstory drifts and maximum interbuilding approaches corresponding to the uncontrolled configuration (black solid line with squares), the active controller defined by the control gain matrix \(\mathbf{K}^{\mathrm{m}}\) (blue solid line with circles), the passive controller defined by the control gain matrix \(\mathbf{\hat{K}}^{\mathrm{m}}\) (blue dashed line with asterisks), the active controller defined by the control gain matrix \(\mathbf{K}^{\mathrm{v}}\) (red solid line with triangles) and the passive controller defined by the control gain matrix \(\mathbf{\hat{K}}^{\mathrm{v}}\) (red dotted line with hexagrams). building \(\mathcal{B}^{(1)}\), which produces a 39.7% of reduction with respect to the uncontrolled response, and by the unlinked configuration CC3 in building \(\mathcal{B}^{(2)}\), with a relative reduction of 43.1%. These acceleration response characteristics are further illustrated by the plots in Figure 15, where the following facts can be clearly appreciated: (i) all the proposed controllers produce positive results in reducing the story absolute acceleration peak-values when compared with the uncontrolled response; (ii) the unlinked control configuration CC3 is more effective in mitigating the acceleration response of the taller building \(\mathcal{B}^{(2)}\); (iii) the linked control configuration CC4 attains better results in reducing the acceleration response of the shorter building \(\mathcal{B}^{(1)}\); and (iv) the levels of performance of the passive controllers are similar to those attained by the corresponding active controllers, especially in the case of the linked control configuration CC4. **Remark 2**: _In order to avoid the modeling and simulation difficulties associated to interbuilding collisions, the numerical simulations have been carried out assuming that the interbuilding spacing is large enough to prevent bounding events. In this case, the maximum interbuilding approaches can be understood as lower bounds of safe interbuilding distances. Thus, for example, the central plots in Figure 14 point out that, for the considered seismic event, an interbuilding distance of 2.5 cm can be considered safe for the active and passive controllers