Local Lyapunov functions for periodic and finite-time ODEs

Giesl, Peter and Hafstein, Sigurdur (2013) Local Lyapunov functions for periodic and finite-time ODEs. In: Johann, Andreas, Kruse, Hans-Peter, Rupp, Florian and Schmitz, Stephan (eds.) Recent Trends in Dynamical Systems. Springer Proceedings in Mathematics & Statistics . Springer, Basel, pp. 125-152. ISBN 9783034804509

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Abstract

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.

Item Type: Book Section
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Peter Giesl
Date Deposited: 16 Jun 2015 17:00
Last Modified: 16 Jun 2015 17:00
URI: http://sro.sussex.ac.uk/id/eprint/54588
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