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.
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Bibliography
More information about stability theory for hybrid dynamical systems, and related systems, can be found in selected books and journal papers from the stability and control literature.
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Teel, A.R. (2013). Stability Theory for Hybrid Dynamical Systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_99-1
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_99-1
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Publisher Name: Springer, London
Online ISBN: 978-1-4471-5102-9
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Latest
Stability Theory for Hybrid Dynamical Systems- Published:
- 16 January 2020
DOI: https://doi.org/10.1007/978-1-4471-5102-9_99-2
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Original
Stability Theory for Hybrid Dynamical Systems- Published:
- 03 April 2014
DOI: https://doi.org/10.1007/978-1-4471-5102-9_99-1