On Distributed Prescribed-Time Unknown Input Observers

This article is concerned with the design of the distributed prescribed-time unknown input observer (DPTUIO) for a class of linear time-invariant systems, which we refer to as the target systems. Results on distributed unknown input observers in literature did not address the convergence time predefinition problem. To achieve fast estimation, this article uses weakly unobservable subspace decomposition and introduces a time-scale transformation technology to develop a novel DPTUIO. This design ensures that, for each node, the entire state of the target system can be estimated within a preassigned time, despite each node measuring only a small portion of the systems output. Detailed discussions on the existence conditions of the DPTUIO are provided. It is established that the observer matching condition, along with the jointly strongly observability condition and a strongly connected communication network, constitutes sufficient conditions for the existence of the DPTUIO. Moreover, the robustness of the developed DPTUIO against measurement and communication noise is analyzed in detail with rigorous deduction. Finally, a practical example is used to verify the effectiveness of the proposed methods.