  In this work, we present a compositional safety controller synthesis approach
for the class of discrete-time linear control systems. Here, we leverage a
state-of-the-art result on the computation of robust controlled invariant sets.
To tackle the complexity of controller synthesis over complex interconnected
systems, this paper introduces a decentralized controller synthesis scheme.
Rather than treating the interconnected system as a whole, we first design
local safety controllers for each subsystem separately to enforce local safety
properties, with polytopic state and input constraints as well as bounded
disturbance set. Then, by composing the local controllers, the interconnected
system is guaranteed to satisfy the overall safety specification. Finally, we
provide a vehicular platooning example to illustrate the effectiveness of the
proposed approach by solving the overall safety controller synthesis problem by
computing less complex local safety controllers for subsystems and then
composing them.
