Cooperative Stabilization Control of the Linear Time-invariant System Based on Distributed Observers

In this paper, the cooperative stabilization problem of linear time-invariant (LTI) systems is studied based on a class of distributed Luenberger observers. A given LTI system is estimated by a network of observers. In case of observability configuration or external attack, each observer has to possess different measurement output of the LTI system. Classical distributed control strategies cannot be directly used because they are assumed to obtain identical information. In view of this problem, a class of distributed observers are designed under an undirected graph, which can recover the state of the LTI system by limited local information. By using any single channel of the estimated state, a control input is proposed to stabilize the LTI system. By analysing the stability of an augmented system which involves the LTI system and the estimation error system, some necessary and sufficient conditions arc derived for the existence of control gains that guarantee the stabilization of the LTI system. In addition, some algorithms are proposed to specify the control gains. Lastly, some simulation examples are given to verify the effectiveness of the theoretical result.