A Note on Controllability of Directed Networked MIMO Systems With Heterogeneous Dynamics
Abhijith Ajayakumar, Raju K. George · IEEE Transactions on Control of Network Systems · 2022
In 2020, Xiang et al. derived a necessary condition for the controllability of a special type of heterogeneous networked system. Theorem 3 in Xiang et al. states that the observability of each node is necessary for the controllability of a heterogeneous networked system satisfying: 1) similar state matrices; 2) that output matrices are scalar multiples of one another; and 3) that the rank of the input matrix of the networked system is less than the number of nodes in the system. In this article, we have given a counterexample to show that this claim is not true in general. Furthermore, we have given a necessary condition for the controllability of a heterogeneous networked system with aforementioned properties. The obtained result is demonstrated through examples.