Improved bounds on the stability margin of dynamical networks

Stability margin is a classical measure that quantifies robustness of a dynamical system for various types of perturbations. In this paper we improve bounds on the stability margin of undirected networks with SISO (Single-Input-Single-Output) local dynamics. These improved bounds can be exploited for design and modification of dynamical networks in a robust manner. Here, first we show that only a certain part of Nyquist plot of network's local dynamics should be considered for obtaining network stability margin. Second, using the first result we find a tighter lower-bound on the stability margin of dynamical networks. Finally, we find a tight upper-bound for networks with a specific type of local dynamics. Several examples of network topology design and alteration problems are presented to demonstrate the effectiveness of the obtained results.