  A Multi-hop Control Network consists of a plant where the communication
between sensors, actuators and computational units is supported by a (wireless)
multi-hop communication network, and data flow is performed using scheduling
and routing of sensing and actuation data. Given a SISO LTI plant, we will
address the problem of co-designing a digital controller and the network
parameters (scheduling and routing) in order to guarantee stability and
maximize a performance metric on the transient response to a step input, with
constraints on the control effort, on the output overshoot and on the bandwidth
of the communication channel. We show that the above optimization problem is a
polynomial optimization problem, which is generally NP-hard. We provide
sufficient conditions on the network topology, scheduling and routing such that
it is computationally feasible, namely such that it reduces to a convex
optimization problem.
