Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Stability Theory for Hybrid Dynamical Systems

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_99-1

Abstract

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.

Keywords

Hybrid system Asymptotic stability Basin of attraction Lyapunov function 
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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

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