State estimation constitutes a core task in monitoring, supervision, and control of dynamic systems. This paper proposes a data-driven framework for the design of state observers for descriptor systems. Necessary and sufficient conditions for the existence of a standard state observer are derived purely from data under mild assumptions. When the system is subject to unknown inputs, we further extend the framework to the data-driven design method for full-order unknown input observer (UIO). Notably, for both the standard state observer and the UIO, we establish the mathematical equivalence between the proposed data-driven existence conditions and classical model-based ones. Moreover, the data-driven approach is applied to the design of extended state observers, enabling simultaneous estimation of system states and disturbances via system augmentation. Numerical simulations validate the effectiveness of the proposed methods.
@article{arxiv.2604.11345,
title = {Data-Driven Observers Design for Descriptor Systems},
author = {Yuan Zhang and Yu Wang and Keke Huang and Zhongqi Sun and Tyrone Fernando},
journal= {arXiv preprint arXiv:2604.11345},
year = {2026}
}