Distributed State Estimation under Jointly Connected Switching Networks: Continuous-Time Linear Systems and Discrete-Time Linear Systems

In this article, we address the distributed state estimation problem for both continuous-time linear time-invariant (LTI) systems and discrete-time LTI systems under switching networks. The observed system is jointly observable, i.e., each agent can only access a part of the measurement output of the observed system and cannot recover the full state by itself. The full state estimation has to be achieved by network communication of neighboring agents. In contrast to existing works, the salient feature of this work is that the developed approach can deal with jointly connected switching networks and thus is more resilient to unreliable communication. First, we propose a new observability decomposition method for linear systems in modal canonical form. Then, we design distributed observers for both the continuous-time system and the discrete-time system. Based on the common Lyapunov function approach, we show that the switched estimation error system is asymptotically stable and thus, the full state estimation can be achieved under jointly connected switching networks.