On Distributed Observer Design of a Descriptor System

In this paper, the problem of how to design a distributed observer for a regular descriptor linear system (i.e., named as the targeted system in this paper) is considered. The outputs of the descriptor system is measured by a group of agents, where each agent can only measure a part of outputs and cannot guarantee the complete observability of the targeted system. This indicates that each local observer in the network can access a portion of the targeted system's output only and interacts with neighboring nodes based on the given network. Furthermore, there is no effect on the estimation of the descriptor state while the number of agents increases or decreases. We recover the established result that a distributed observer exists if the regular descriptor system is completely observable and the network graph is a strongly connected directed graph. The main idea is to estimate the descriptor plant by recovering the completely observable component of each agent and measuring the completely unobservable component through the information interaction between nodes of the multi-agent network.