A modified quadratic performance criterion for the optimal control of linear systems is proposed. This criterion includes terms which allow the designer to penalize deviations of states, outputs, and controls according to their sign, as well as their squared value. The optimal state regulator, output regulator, and output tracker with finite final time are developed for this performance criterion, and are found to consist of a feedback control and an open-loop control. It is shown that reduction of these laws to the infinite-time regulator case is not possible. The application of these control laws to a two-effect evaporator model is shown as an example.