File(s) not publicly available
Local Lyapunov functions for periodic and finite-time ODEs
Lyapunov functions for general systems are difficult to construct. However, for autonomous linear systems with exponentially stable equilibrium, there is a classical way to construct a global Lyapunov function by solving a matrix equation. Consequently, the same function is a local Lyapunov function for a nonlinear system. In this paper, we generalise these results to time-periodic and, in particular, finite time systems with an exponentially attractive zero solution. We show the existence of local Lyapunov functions for nonlinear systems. For finite-time systems, we consider a generalised notion of a Lyapunov function, which is not necessarily continuously differentiable, but just locally Lipschitz continuous; the derivative is then replaced by the Dini derivative.
History
Publication status
- Published
Publisher
SpringerExternal DOI
Page range
125-152Book title
Recent Trends in Dynamical SystemsPlace of publication
BaselISBN
9783034804509Series
Springer Proceedings in Mathematics & StatisticsDepartment affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Editors
Florian Rupp, Andreas Johann, Hans-Peter Kruse, Stephan SchmitzLegacy Posted Date
2015-06-16Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC