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Erschienen in:
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2015 | OriginalPaper | Buchkapitel

6. Finite-Dimensional Dynamical Systems

verfasst von : Anthony N. Michel, Ling Hou, Derong Liu

Erschienen in: Stability of Dynamical Systems

Verlag: Springer International Publishing

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Abstract

We present the principal stability and boundedness results for continuous dynamical systems, discrete-time dynamical systems, and discontinuous dynamical systems involving monotonic and non-monotonic Lyapunov functions. We apply the results of Chapter 3 to arrive at these results. When considering various stability types, our focus is on invariant sets that are equilibria. Our results constitute sufficient conditions (the Principal Stability and Boundedness Results) and necessary conditions (Converse Theorems). We demonstrate the applicability of all results by means of numerous examples.
We also present results for uniform stability and for uniform asymptotic stability in the large involving multiple non-monotonic Lyapunov functions. The applicability of these results is demonstrated by means of a specific example.

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Vorheriges Kapitel Applications to a Class of Discrete-Event Systems
Nächstes Kapitel Finite-Dimensional Dynamical Systems: Specialized Results
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Metadaten
Titel
Finite-Dimensional Dynamical Systems
verfasst von
Anthony N. Michel
Ling Hou
Derong Liu
Copyright-Jahr
2015
Buch
Stability of Dynamical Systems

Print ISBN: 978-3-319-15274-5

Electronic ISBN: 978-3-319-15275-2

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-15275-2_6

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