On Node Controllability and Observability in Complex Dynamical Networks

We analyze in detail the subtle yet critical differences between the controllability and observability properties of the triplet (A, B, C) in the two cases that this is viewed as a network of dynamical nodes or as a single complex system. We show that investigating the controllability and observability properties of each single node when the network is not completely controllable and/or observable, requires the development of novel tools leading, ultimately, to a network decomposition that is different from the state-space decomposition proposed in 1963 by Kalman for linear systems.