## 4 Numerical Simulations
Looking at graphics in Figures 11 and 12a, the following facts can be clearly appreciated: (i) all the controllers provide a significant level of reduction in the interstory drift and interbuilding approach peak-values when compared with the uncontrolled response; (ii) the unlinked control configuration CC1 is more effective in mitigating the interstory drift response; (iii) the linked control configuration CC2 attains better results in reducing the interbuilding approaches; (iv) smaller control-effort peak-values are produced by the linked configuration CC2; and (v) the levels of performance attained by the passive controllers are quite similar to those achieved by the corresponding active controllers, especially in the case of the linked control configuration CC2. Figure 10: Full-scale North-South El Centro 1940 ground acceleration seismic record. For the control configurations with three actuation devices CC3 and CC4, the plots of interstory drift and interbuilding approach peak-values presented in Figure 13 show that the best overall behavior corresponds to the linked control configuration CC4 with the active controller defined by the control gain matrix \(\mathbf{K}^{\mathrm{v}}\) given in Equation (41) (red solid line with triangles). Also remarkable is the overall performance of the linked control configuration CC4 with the passive controller defined by the control gain matrix \(\mathbf{\hat{K}}^{\mathrm{v}}\) given in Table 3 (red dotted line with hexagrams). Moreover, looking at the plots shown in Figure 12b, it can be appreciated that smaller control-effort peak-values are required by the controllers corresponding to the linked control configuration CC4. For the control configurations with four actuation devices CC5 and CC6, the plots of interstory drift and interbuilding approach peak-values presented in Figure 14 and the control-effort peak-values displayed in Figure 12c indicate the superior performance of the linked control configuration CC6 with the active controller defined by the control gain matrix \(\mathbf{K}^{\mathrm{v}}\) given in Equation (43). The good properties of this linked control configuration with the passive controller \(\mathbf{\hat{K}}^{\mathrm{v}}\) can also be clearly appreciated. It should be recalled that feasibility issues appeared in the design of a fully decentralized velocity-feedback controller for the unlinked control configuration CC5 and, consequently, no passive controller is available for this case. Figure 11: _Interstory drift and interbuilding approach peak-values for the control configurations CC1 and CC2. 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 \(\mathbf{K}^{\mathrm{i}}\) (blue solid line with circles), the passive controller defined by the control gain matrix \(\mathbf{\hat{K}}^{\mathrm{i}}\) (blue dashed line with asterisks), the active controller defined by the control gain matrix \(\mathbf{K}^{\mathrm{n}}\) (red solid line with triangles) and the passive controller defined by the control gain matrix \(\mathbf{\hat{K}}^{\mathrm{n}}\) (red dotted line with hexagrams)._  
Figure 12: _Maximum absolute control efforts._ (**a**) Configurations with two actuation devices: CC1 (unlinked) and CC2 (linked). (**b**) Configurations with three actuation devices: CC3 (unlinked) and CC4 (linked). (**c**) Configurations with four actuation devices: CC5 (unlinked) and CC6 (linked). To complement the information supplied by the interstory drift and the interbuilding approach time responses, the absolute acceleration peak-values of the buildings' top-level stories corresponding to the proposed active and passive velocity-feedback controllers are presented in Tables 5 and 6, respectively.