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Case Studies

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Networks of Dissipative Systems

Part of the book series: SpringerBriefs in Electrical and Computer Engineering ((BRIEFSCONTROL))

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Abstract

This chapter illustrates the equilibrium-independent stability analysis technique of the previous chapter with four case studies. The first one is a biochemical reaction network with a cyclic interconnection structure. The second one is a vehicle platoon where the motion of the vehicles is coordinated with relative position feedback. The third one is Internet congestion control with decentralized user and router algorithms. The vehicle platoon and congestion control examples exhibit a skew-symmetric coupling structure which means that passivity of the subsystems guarantees network stability. The fourth case study on population dynamics studies interaction structures between multiple species described by cactus graphs.

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Notes

  1. 1.

    For example, the strict concavity condition (4.21) is sufficient for the existence of a unique equilibrium [5].

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA, USA

    Murat Arcak

  2. Department of Mechanical Engineering, University of California, Berkeley, Berkeley, CA, USA

    Chris Meissen & Andrew Packard

Authors
  1. Murat Arcak
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  2. Chris Meissen
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  3. Andrew Packard
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Correspondence to Murat Arcak .

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Arcak, M., Meissen, C., Packard, A. (2016). Case Studies. In: Networks of Dissipative Systems. SpringerBriefs in Electrical and Computer Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-29928-0_4

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  • DOI: https://doi.org/10.1007/978-3-319-29928-0_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29927-3

  • Online ISBN: 978-3-319-29928-0

  • eBook Packages: EngineeringEngineering (R0)

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