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Input-to-state stability for a class of hybrid dynamical systems via averaging

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Abstract

Input-to-state stability (ISS) properties for a class of time-varying hybrid dynamical systems via averaging method are considered. Two definitions of averages, strong average and weak average, are used to approximate the time-varying hybrid systems with time-invariant hybrid systems. Closeness of solutions between the time-varying system and solutions of its weak or strong average on compact time domains is given under the assumption of forward completeness for the average system. We also show that ISS of the strong average implies semi-global practical (SGP)-ISS of the actual system. In a similar fashion, ISS of the weak average implies semi-global practical derivative ISS (SGP-DISS) of the actual system. Through a power converter example, we show that the main results can be used in a framework for a systematic design of hybrid feedbacks for pulse-width modulated control systems.

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Authors and Affiliations

  1. Electrical and Electronic Engineering Department, The University of Melbourne, Melbourne, VIC, 3010, Australia

    Wei Wang & Dragan Nešić

  2. Electrical and Computer Engineering Department, University of California at Santa Barbara, Santa Barbara, CA, 93106-9560, USA

    Andrew R. Teel

Authors
  1. Wei Wang
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  2. Dragan Nešić
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  3. Andrew R. Teel
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Corresponding author

Correspondence to Wei Wang.

Additional information

This study was supported by the Australian Research Council under the Discovery Project, Future Fellow program, AFOSR (Grant FA9550-09-1-0203) and NSF (Grants ECCS-0925637 and CNS-0720842).

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Wang, W., Nešić, D. & Teel, A.R. Input-to-state stability for a class of hybrid dynamical systems via averaging. Math. Control Signals Syst. 23, 223–256 (2012). https://doi.org/10.1007/s00498-011-0070-y

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  • DOI: https://doi.org/10.1007/s00498-011-0070-y

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