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Scalable decentralized robust stability certificates for networks of interconnected heterogeneous dynamical systems

Lestas I. and Vinnicombe G.

November 2004
Technical Report: CUED/F-INFENG/TR.501

Abstract

We derive scalable decentralized conditions that guarantee robust stability for networks of linearly interconnected, stable, linear time invariant dynamical systems. Participating dynamics are only required to know the dynamics of their neighbours, therefore, the stability certificates are scalable to the network size and the way it is interconnected, which is a distinctive feature of this work. Unlike previous scalability results, heterogeneous dynamics in arbitrary interconnection protocols are considered. A structure in the underlying graph, e.g. a bipartite graph, leads to less conservative conditions and we also show that a break of symmetry affects only locally the stronger stability certificates for symmetric networks. It is illustrated with a random graph example that the conditions are not too conservative in large scale networks with small connectivity. Finally, an application of this theory is given, where robustness analysis of Internet congestion control protocols is carried out in the general case of dynamics at both users and resources without any global bounds on the dynamics.

BibTex Entry

@TechReport{,: author = {Lestas I. and Vinnicombe G.},; institution = {Cambridge University, Engineering Department},; title = {Scalable decentralized robust stability certificates for networks of interconnected heterogeneous dynamical systems},; year = {2004},; month = {November},; note = {CUED/F-INFENG/TR.501}
}



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