In this paper, we incorporate the placement of one real closed-loop po
le into a compensator design framework based upon the Youla parameteri
zation, duality theory, and linear programming, This framework has bee
n used to design discrete-time compensators to solve the l(1) controll
er design problem as well as other related time-domain optimization pr
oblems. Previous work on these problems has focused on deadbeat system
s, It is known that these can require high-order controllers. Part of
the motivation for this work is to improve the tradeoff between contro
ller order and performance over that using deadbeat control.