Distributed Observer with Lower Dimension Local Observer for Large-Scale LTI Systems*

The use of distributed observer enables states omniscience, which allows distributed-observer-based distributed control laws to achieve the same control performance as centralized control laws. However, this advantage comes at the cost of increasing the dimension of local observers on each agent to match that of the entire interconnected large-scale system. This contradicts the original intention of the distribution strategy. This paper proposes a solution to this problem through the development of a partitioned distributed observer. By designing a partition algorithm for the large-scale system, the system is divided into multiple intersecting partitions. Additionally, a distributed observer is implemented within each partition, and a two-layer Lyapunov method is employed to ensure the stability of the error dynamics of the partitioned distributed observer. As a result, not only is the dimension of the local observer significantly reduced compared to that of the large-scale system, but the partitioned distributed observer also achieves the same performance as the traditional state omniscience distributed observer. Simulation results validate the effectiveness of the proposed theory.