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

Minimum jointly structural input and output selection for strongly connected networks