Data-based analysis methods for the state controllability and state observability of discrete-time LTI systems with time-delays

We present a couple of data-based methods to analyze the state controllability and state observability of discrete-time Linear time-Invariant (LTI) systems with time-delays, which have unknown parameter matrices. They first augment the system into a high dimensional LTI model, then apply the measured state and output data to directly build the controllability and observability matrices respectively of this high dimensional model, whose ranks are used as the criteria of the corresponding properties of the system before augmentation. These data-based methods have low computational load and calculation complexity.