In practical control systems, the capacity of actuators is limited and this degrades the system performances and it is often a source of instability. To use full capacity of actuators, we adopt the gain scheduled control permitting the over saturation in controls. The basic idea of gain scheduled control is to use a higher gain control when the state variables are smaller and a lower gain control when the state variables are larger. First, we derive a constant H control and a reachable set while satisfying the degree of over saturation. Next, we divide this set into nested subsets and find $H_{infty}$ controls at rack subsets while satisfying the degree of over saturation. Finally, the control gain is applied according to the status of states. Note that all procedures are done by solving linear matrix inequalities(LMI). Finally, we show the validity and applicability of our proposed control using the simulations of a six-story building subjected to the earthquake excitation.