  How to realize high-level autonomy of individuals is one of key technical
issues to promote swarm intelligence of multi-agent (node) systems with
collective tasks, while the fully distributed design is a potential way to
achieve this goal. This paper works on the fully distributed state estimation
and cooperative stabilization problem of linear time-invariant (LTI) plants
with multiple nodes communicating over general directed graphs, and is aimed to
provide a fully distributed framework for each node to perform cooperative
stabilization tasks. First, by incorporating a novel adaptive law, a
consensus-based estimator is designed for each node to obtain the plant state
based on its local measurement and local interaction with neighbors, without
using any global information of the communication topology. Subsequently, a
local controller is developed for each node to stabilize the plant
collaboratively with performance guaranteed under mild conditions.
Specifically, the proposed method only requires that the communication graph be
strongly connected, and the plant be collectively controllable and observable.
Further, the proposed method can be applied to pure fully distributed state
estimation scenarios and modified for noise-bounded LTI plants. Finally, two
numerical examples are provided to show the effectiveness of the theoretical
results.
