A Decentralized Designed Distributed Observer for Linear Interconnected Systems

This article addresses the problem of distributed state estimation (DSE) for discrete-time interconnected systems, where the observed system is composed of subsystems interconnected through state-to-state and state-to-output couplings. Inspired by the leader-follower consensus method, we propose a distributed observer that enables each subsystem to estimate the entire state of the interconnected system. Under certain structural assumptions, we derive necessary and sufficient conditions for the stability of the estimation error dynamics. We further present a decentralized design of the proposed observer, where the operation and construction of the observer can be completed by each subsystem using its locally available information, including the system's basic configuration, local measurements, and data exchanged with neighboring subsystems. In addition, we demonstrate that our distributed estimation framework can be applied to solve the distributed estimation problem for linear time-invariant (LTI) systems with fixed composition by employing an observability decomposition method. Finally, we illustrate the effectiveness of our scheme by applying it to vehicle platooning.