Distributed Observer Design for Linear Systems under Time-Varying Communication Delay

The paper investigates the state estimation problem of general continuous-time linear systems with the consideration of time-varying communication delay. A solution is proposed in terms of the networked distributed observer, which consists of multiple local observers. Each local observer relies on only part of the system output and exchanges information with neighbors through undirected links modeled by a prespecified communication graph. A simple approach for computing observer parameters is presented by solving a parametric algebraic Riccati equation. Furthermore, by the Lyapunov–Krasovskii stability theorem, an upper bound of the delay could be calculated explicitly and together with the conditions of joint observability and connectivity of the communication graph; the resulting distributed observers work coordinately to achieve an asymptotic estimate of the full plant state. An illustrative example is provided to confirm the analytical results.