Data-based controllability analysis for generalised linear discrete-time system

In this paper, we aim to propose a data-based method to testify whether the system is a normal linear system or a generalised linear system and then analyse its controllability via the measured state data and the control input satisfying certain condition. For this purpose, we first describe a linear discrete-time system in a general form and derive a necessary and sufficient condition for the equivalent condition of complete controllability with a normal linear discrete time system. Second, we check whether the system is normal or singular, and then construct the controllability matrices only based on the input and measured state data. Third, the controllability of the corresponding system is investigated thoroughly based on available data without identifying system parameters. Finally, a numerical example and a stock price example are used to show the effectiveness and feasibility of the proposed data-based method.