  We study the design of scheduling logic and control logic for networked
control systems (NCSs) where plants communicate with their remotely located
controllers over a shared band-limited communication network. Due to a limited
capacity of the network, only a subset of the plants can exchange information
with their controllers at any instant of time and the remaining plants operate
in open-loop. Our key contribution is a new algorithm that co-designs (a) an
allocation scheme of the communication network among the plants (scheduling
logic) and (b) the control inputs for the plants accessing the network (control
logic) under which given non-zero initial states are steered to zero in a given
time horizon for all the plants in the NCS. Sparse optimization is the primary
apparatus for our analysis. We also provide sufficient conditions on the plant
dynamics, capacity of the communication network and the given time horizon that
lead to a numerically tractable implementation of our algorithm. A numerical
experiment is presented to demonstrate the proposed results.
