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Asymptotic Stability of Switched Higher Order Laplacians

  • Abubakr Muhammad
  • Ali Jadbabaie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4416)

Abstract

Recently, several properties in networked sensing and distributed systems have been modeled by various researchers [1,2,3,5,7,9,11,12] using topological spaces and their topological invariants. The unifying theme in these approaches has been that the local properties of a network, as dictated by local interactions among agents, can be captured by certain topological spaces. These spaces are mostly combinatorial in nature and are a generalization of the more familiar graphical models. Moreover, the global properties of the network characteristics correspond to certain topological invariants of these spaces such as genus, homology, homotopy, and the existence of simplicial maps. Examples of such modeling attempts include coverage problems for sensor networks [1,2,3,7]; consensus & concurrency modeling in asynchronous distributed systems [9]; and routing in networks without geographical information [5]. One notable characteristic of these studies has been that the topological abstractions preserve many global geometrical properties of the network while abstracting away the redundant geometrical details at small scales. This promises great simplification of algorithms as well as hardware, which is an important requirement for realizing large-scale robust networks.

Keywords

Sensor Network Asymptotic Stability Simplicial Complex Homology Group Topological Invariant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Abubakr Muhammad
    • 1
  • Ali Jadbabaie
    • 1
  1. 1.Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104USA

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