Decentralized Design of Distributed Observers for LTI Systems

This note proposes a novel decentralized/decomposed design of distributed observers for general continuous-time linear time invariant systems. Each observer can only observe a portion of the system. By transforming the system to a real Jordan canonical form, an observability decomposition is performed based on Popov-Belevitch-Hautus test. Each observer reconstructs observable states from its local measurements. The unobservable states are reconstructed relying on a communication network, by virtue of synchronizing region design in pinning control theory. The required graph connectivity is milder than strongly connected graphs. The proposed design is decentralized in the sense that its computational complexity is decomposed via solving lower-dimensionality algebraic Riccati equations. The computational complexity is thus independent of the total number of agents in the graph, exhibiting a high level of scalability on large networks. Another key feature of the proposed design is that the convergence rate of estimation errors can be tuned to be arbitrarily fast. Numerical simulations demonstrate the design procedure and the corresponding performance.