  In this paper, given a linear time-invariant strongly connected network, we
study the problem of determining the minimum number of state variables that
need to be simultaneously actuated and measured to ensure structural
controllability and observability, respectively. This problem is fundamental in
the design of multi-agent systems, where there are economic constraints in the
decision of which agents to equip with a more costly on-board system that will
allow the agent to have both actuation and sensing capabilities. Despite the
combinatorial nature of this problem, we present a solution that couples the
design of both structural controllability and structural observability
counterparts to address it with polynomial-time complexity.
