10-3934-dcdsb-2015-20-2291-post-ref-version.pdf (738.14 kB)
Review on computational methods for Lyapunov functions
journal contribution
posted on 2023-06-08, 22:59 authored by Peter GieslPeter Giesl, Sigurdur HafsteinLyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function.
History
Publication status
- Published
File Version
- Accepted version
Journal
Discrete and Continuous Dynamical Systems - Series BISSN
1531-3492Publisher
American Institute of Mathematical SciencesExternal DOI
Issue
8Volume
20Page range
2291-2331Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2016-01-12First Open Access (FOA) Date
2016-11-01First Compliant Deposit (FCD) Date
2015-10-29Usage metrics
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