On the scalable stability of nonsymmetric heterogeneous networks

Underlying interconnection symmetry is often a major assumption for the derivation of scalable decentralized stability certificates in networks i.e. decentralized stability guarantees for an arbitrary interconnection of heterogeneous dynamical systems. Even though such symmetry simplifies significantly the mathematical analysis it is often the case that networks can behave robustly even when deviations from protocol symmetry do occur. We show in this paper how spectral inclusion techniques can be used to certify scalable stability in classes of nonsymmetric networks with potential applications in Internet congestion control and consensus protocols. The certificates derived are decentralized and scale with the degree of nonsymmetry.