Necessary and sufficient conditions of controllability of networked SISO systems with nonidentical dimensional nodes

The controllability of networked systems with nonidentical node dimensions is explored, where the communications are one-dimensional. The effects of nonidentical node dimensions on controllability are discussed. In addition, several necessary and/or sufficient conditions of controllability are provided. Differ from the networked systems with identical node dimensions, nonidentical node dimensions can turn a controllable networked system into an uncontrollable one. Moreover, the necessary and/or sufficient conditions derived for networked systems with self-loop node dynamics and chain node dynamics show that special node dynamics may make the systems easier to be controlled. Besides, some numerical examples and practical application are given to illustrate the feasibility and applicability of the proposed methods.