Fixed-Time Convergent Distributed Observer Design of Linear Systems: A Kernel-Based Approach

Abstract: The robust distributed state estimation for a class of continuous-time linear time-invariant systems is achieved by a novel kernel-based distributed observer, which, for the first time, ensures fixed-time convergence properties. The communication network between the agents is prescribed by a directed graph in which each node involves a fixed-time convergent estimator. The local observer estimates and broadcasts the observable states among neighbours so that the full state vector can be recovered at each node and the estimation error reaches zero after a predefined fixed time in the absence of perturbation. This represents a new distributed estimation framework that enables faster convergence speed and further reduced information exchange compared to a conventional Luenberger-like approach. The ubiquitous time-varying communication delay across the network is suitably compensated by a prediction scheme. Moreover, the robustness of the algorithm in the presence of bounded measurement and process noise is characterised. Numerical simulations and comparisons demonstrate the effectiveness of the observer and its advantages over the existing methods.