On the controllability and observability of networked dynamic systems

Some necessary and sufficient conditions are obtained for the controllability and observability of a networked system with linear time invariant (LTI) dynamics. The topology of this system is fixed but arbitrary, and every subsystem is permitted to have different dynamics. These conditions essentially depend only on transmission zeros of every subsystem and the subsystem connection matrix, which makes them attractive in the analysis and synthesis of a large-scale networked system. As an application, these conditions are utilized to characterize systems whose steady estimation accuracy with the distributed predictor of Zhou (2013) is equal to that of the lumped Kalman filter. It has been made clear that to guarantee this equivalence, the steady update gain matrix of the Kalman filter must be block diagonal.