This paper proposes a modified version of Leitmann and co-authors' classical result on the stabilization of uncertain nonlinear systems. In particular, for usual models of structure dynamics in earthquake engineering it is shown that applying a specific control law drives the state variables into a ball around the origin (arbitrarily chosen) in finite time as long as the radius of the ball is not lower than a limiting value. In addition estimates of this limiting ball radius and the time limit for arbitrary ball radius are provided. The semi-active control thus provides the control designer with interesting design parameters. It is also an attempt to explicitly use pseudoacceleration floor response spectrum as a performance criterion. Though not limited to twodegree- of-freedom structures, this semi-active control is applied to these plant models for simplicity and illustrated through simulations.