Controllability of Multilayer Networked Sampled-Data Systems

The controllability analysis of networked systems is challenging due to their high dimensionality and complex structure. The influence of sampling on network controllability is rarely studied, making it an important topic to explore. In this article, the state controllability of multilayer networked sampled-data systems is studied, considering the deep network structure, multidimensional node dynamics, various inner couplings, and sampling patterns. Necessary and/or sufficient controllability conditions are proposed and validated by numerical and practical examples, requiring less computation than the classic Kalman criterion. Single-rate and multirate sampling patterns are analyzed, showing that adjusting the sampling rate of local channels can affect the controllability of the overall system. It is shown that the pathological sampling of single-node systems can be eliminated by an appropriate design of interlayer structures and inner couplings. In the case of systems with drive-response mode, the overall system may not lose controllability even when the response layer is uncontrollable. The results demonstrate that mutually coupled factors collectively affect the controllability of the multilayer networked sampled-data system.