  This paper considers a strongly connected network of agents, each capable of
partially observing and controlling a discrete-time linear time-invariant (LTI)
system that is jointly observable and controllable. Additionally, agents
collaborate to achieve a shared estimated state, computed as the average of
their local state estimates. Recent studies suggest that increasing the number
of average consensus steps between state estimation updates allows agents to
choose from a wider range of state feedback controllers, thereby potentially
enhancing control performance. However, such approaches require that agents
know the input matrices of all other nodes, and the selection of control gains
is, in general, centralized. Motivated by the limitations of such approaches,
we propose a new technique where: (i) estimation and control gain design is
fully distributed and finite-time, and (ii) agent coordination involves a
finite-time exact average consensus algorithm, allowing arbitrary selection of
estimation convergence rate despite the estimator's distributed nature. We
verify our methodology's effectiveness using illustrative numerical
simulations.
