  In this paper, we propose a new design method of discrete-valued control for
continuous-time linear time-invariant systems based on sum-of-absolute-values
(SOAV) optimization. We first formulate the discrete-valued control design as a
finite-horizon SOAV optimal control, which is an extended version of L1 optimal
control. We then give simple conditions that guarantee the existence,
discreteness, and uniqueness of the SOAV optimal control. Also, we give the
continuity property of the value function, by which we prove the stability of
infinite-horizon model predictive SOAV control systems. We provide a fast
algorithm for the SOAV optimization based on the alternating direction method
of multipliers (ADMM), which has an important advantage in real-time control
computation. A simulation result shows the effectiveness of the proposed
method.
