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From Stability to Performance and Safety

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Networks of Dissipative Systems

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

Abstract

In this chapter we extend the compositional approach from stability analysis to certifying performance and safety. Performance is defined as a desired dissipativity property for the interconnection, such as a prescribed gain from a disturbance input to a performance output. A storage function for the interconnection is synthesized as a weighted sum of subsystem storage functions and the weights are left as decision variables in a linear matrix inequality. Next we address the safety problem where the goal is to guarantee that trajectories starting in a prescribed set do not intersect a given unsafe set under a set of admissible disturbances. This time a weighted sum of subsystem storage functions serves as a barrier function for the interconnection.

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References

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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). From Stability to Performance and Safety. In: Networks of Dissipative Systems. SpringerBriefs in Electrical and Computer Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-29928-0_5

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  • DOI: https://doi.org/10.1007/978-3-319-29928-0_5

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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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