Controllability and observability of discrete linear periodic system based on data-driven methods*

This paper presents a novel data-driven analysis method for studying the state controllability and observability of linear discrete periodic time-varying systems with unknown system properties. The proposed approach first transforms the system into a time-invariant system using lifting transformation. Subsequently, new controllability/observability matrices are constructed from state/output measurements. A key advantage of this method is that it enables the determination of the system's structural properties without relying on the state-space matrices. This avoids the complex computational processes that are typically involved.