Data-Driven Controllability and Observability Tests for Descriptor Systems

This paper proposes rank-based criteria for testing R-controllability and C-controllability, as well as R-observability and C-observability of the discrete-time descriptor (singular) systems using purely input-output data matrices. To address the non-causality-induced challenges in C-controllability analysis, forward and backward data matrices are constructed. Furthermore, Willems' fundamental lemma is extended to incompletely controllable descriptor systems, demonstrating that finite-length trajectories with initial states in specific subspaces can be linearly represented by measured trajectories. Numerical examples validate the effectiveness of the proposed criteria and show that Data-enabled Predictive Control (DeePC) achieves output tracking even under incomplete system controllability for descriptor systems.