On Necessary and Sufficient Conditions for Identifiability and Identification of Switching Dynamical Networks

We consider the identifiability and identification problem of a dynamical network modeled by a switched linear dynamical system governed by a sequence of switchings. We aim at exactly reconstructing the network sequence along with the switching signal from the state trajectories of all nodes. The identification of a switching dynamical network is more challenging than that of a time-invariant dynamical network in that the data is generated by a number of different subsystems at different periods. By observability conditions, we first establish a necessary and sufficient condition for the identifiability of switching dynamical networks. Building on this, a sufficient identification condition is developed leveraging coupled Lyapunov-transpose matrix equations, which allows us to design a new algorithm that can exactly recover the whole network sequence, even if the switching signal is completely unknown a prior. Finally, a numerical example is provided to verify the effectiveness of the theoretical results.