Data-Driven Analysis Methods for Controllability and Observability of A Class of Discrete LTI Systems with Delays

We propose a couple of data-driven analysis methods for the state controllability and state observability of a class of discrete linear time-invariant (LTI) systems with delays, which have unknown parameter matrices. To analyze the state controlla-bility and the state observability, these data-driven methods first transform the system model into an augmented state-space model, and then use the state/output data that were previously measured, to directly build the controllability/observability matrices of this augmented model. Our methods have two main advantages over the traditional model-based characteristics analysis approaches. First, the unknown parameter matrices are not necessary to be identified for verifying the state controllability/observability of the system, but these characteristics can be directly verified according to the measured data, thus our methods have less workload. Second, their computational complexity is lower for the construction of the state controllability/observability matrices.