Distributed state estimation of linear descriptor systems

In this paper, we study the problem of state estimation using a network of distributed observers for continuous-time linear descriptor systems. Remarkably, the network of state observers is obtained as state-space systems even though the underlying distributed system is a linear descriptor system. We derive sufficient conditions in terms of the underlying system matrices for the existence of this network of state observers. The derived sufficient conditions consist of solving a linear matrix inequality, making the design easily implementable. Moreover, we introduce the notion of joint detectability of the original system and show that it is necessary for the design of the distributed observers. Finally, the developed theory is illustrated with a numerical example.