Controllability Analysis for a Networked Dynamic System with Autonomous Subsystems

This technical note investigates the controllability of networked dynamic systems of which some subsystems are not directly affected by external inputs (i.e., autonomous). The topology can be arbitrary, and every subsystem can have different dynamics and even different number of states, inputs and outputs. We show that to guarantee the controllability of the whole system, every subsystem should be controllable when isolated. We establish some necessary and sufficient conditions for the system to be controllable. These conditions essentially depend on the parameters of every subsystem separately or the strongly connected autonomous subsystems, which reduce significantly computation complexity for large-scale networked systems. We reveal that heterogenous networked systems under some assumptions can be separated into several independent subnetworks, such that the controllability of the whole system is equal to the controllability of each subnetwork. Based on these conditions, criteria that can be easily verified are given for the controllability of networked systems with some special topologies.