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Relaxation Results for Hybrid Inclusions

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Abstract

The Filippov–Ważewski relaxation theorem describes when the set of solutions to a differential inclusion is dense in the set of solutions to the relaxed (convexified) differential inclusion. This paper establishes relaxation results for a broad range of hybrid systems which combine differential inclusions, difference inclusions, and constraints on the continuous and discrete motions induced by these inclusions. The relaxation results are used to deduce continuous dependence on initial conditions of the sets of solutions to hybrid systems.

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Authors and Affiliations

  1. Department of Electrical & Computer Engineering, University of California, Santa Barbara, CA, 93106, USA

    Chaohong Cai & Andrew R. Teel

  2. 3518 NE 42 St., Seattle, WA, 98105, USA

    Rafal Goebel

Authors
  1. Chaohong Cai
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  2. Rafal Goebel
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  3. Andrew R. Teel
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Corresponding author

Correspondence to Rafal Goebel.

Additional information

Research supported in part by NSF Grants CCR-0311084 and ECS-0622253 and AFOSR Grant FA9550-06-1-0134.

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Cai, C., Goebel, R. & Teel, A.R. Relaxation Results for Hybrid Inclusions. Set-Valued Anal 16, 733–757 (2008). https://doi.org/10.1007/s11228-007-0067-3

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  • DOI: https://doi.org/10.1007/s11228-007-0067-3

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