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Brief Review of Dissipativity Theory

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Networks of Dissipative Systems

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

Abstract

This chapter reviews concepts from dissipativity theory that are foundational for the subsequent chapters. It first gives the general definition and, next, discusses special types of dissipativity that describe finite \(L_2\) gain, passivity, and output strict passivity properties, followed by a graphical interpretation of each type for memoryless systems. The next topic is differential characterization of dissipativity and its specialization to linear systems. This is followed by numerical techniques for certifying dissipativity via semidefinite programming. The final section illustrates the use of dissipativity for reachability and Lyapunov stability analysis.

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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). Brief Review of Dissipativity Theory. In: Networks of Dissipative Systems. SpringerBriefs in Electrical and Computer Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-29928-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-29928-0_1

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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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