On the Phase Margin of Networked Dynamical Systems and Fabricated Attacks of an Intruder

This paper provides a framework to characterize the phase margin of linear time-invariant networked dynamical system where the interaction topology is described by a directed graph. The stability analysis based on the generalized Nyquist theorem is converted to a constrained minimization problem with the help of mapping between two unitary vectors on complex parameter space which is solved to calculate the phase margin of the networked dynamical systems. The resulting phase margin gives sufficient conditions for the closed-loop stability of the networked dynamical system in the presence of complex frequency-dependent perturbations. Further, the impact of malicious agent in the network topology which acts as disturbance generator on the overall network of dynamical systems is analyzed.