Necessary and sufficient conditions of controllability of networked sampled-data systems with nonidentical dimensional nodes

The controllability of completely heterogeneous networked sampled-data systems is investigated in this paper, in which the dimension of nodes is different. Due to the difference of the node dimension, the existing controllability criteria suitable for networked sampled-data systems with identical node dimensions cannot be directly applied to the networks. Besides, node dynamics and couplings between nodes make the pathological sampling on node systems different from networked systems. The pathological sampling of node systems may be eliminated in the whole networked sampled-data systems. That is, even if the node systems lose controllability after pathological sampling, the whole networked sampled-data systems can still maintain controllability. Based on the above analysis, several sufficient and/or necessary conditions verified by low-dimensional matrix operations are provided based on the classic controllability criteria, which require lower computational complexity than the classic controllability criteria. From the results, it can be seen that if the networked systems have typical structures, they are easier to be controllable. The methods presented in this paper are verified by some numerical examples, which also shows the applicability of these conditions.