LAUSR

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.