Topology-free stability of a steady state in network systems with dynamic connections

This paper investigates the robust stability of a steady state in network systems with dynamic connections. A linear stability analysis reveals that the odd number property holds for any network topology. It is shown that the stability of the steady state in network systems with topological uncertainty is governed by the interval family of real characteristic polynomials. A parametric approach, which plays an important role in the field of robust control theory, allows us to analyze the robust stability against the network topological uncertainty. The stability of the steady state, which is valid for any arbitrary topology, can be evaluated by examining at most four characteristic polynomials. These analytical results are applied to coupled Rössler oscillators on a small-world network.