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Local Lyapunov functions for periodic and finite-time ODEs

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posted on 2023-06-08, 21:10 authored by Peter GieslPeter Giesl, Sigurdur Hafstein
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

Springer

Page range

125-152

Book title

Recent Trends in Dynamical Systems

Place of publication

Basel

ISBN

9783034804509

Series

Springer Proceedings in Mathematics & Statistics

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Editors

Florian Rupp, Andreas Johann, Hans-Peter Kruse, Stephan Schmitz

Legacy Posted Date

2015-06-16

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