Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Stability Theory for Hybrid Dynamical Systems

  • Andrew R. TeelEmail author
Living reference work entry

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DOI: https://doi.org/10.1007/978-1-4471-5102-9_99-2


This entry provides a short introduction to modeling of hybrid dynamical systems and then focuses on stability theory for these systems. It provides definitions of asymptotic stability, basin of attraction, and uniform asymptotic stability for a compact set. It points out mild assumptions under which different characterizations of asymptotic stability are equivalent, as well as when an asymptotically stable compact set exists. It also summarizes necessary and sufficient conditions for asymptotic stability in terms of Lyapunov functions.


Asymptotic stability Basin of attraction Hybrid system Lyapunov function 
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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  1. 1.Electrical and Computer Engineering DepartmentUniversity of CaliforniaSanta BarbaraUSA

Section editors and affiliations

  • Francoise Lamnabhi-Lagarrigue
    • 1
  1. 1.Laboratoire des Signaux et SystèmesCNRSGif-sur-YvetteFrance