Fabian Wirth, Diederich Hinrichsen
Further results on the Lyapunov spectrum of time-varying linear discrete-time systems
Preprint series: Proceedings of the Symposium on Mathematical Theory of Networks and Systems MTNS-2000, Perpignan, France, 2000
MSC:
34D08 Lyapunov exponents
93C55 Discrete-time
Abstract:
We continue our analysis of the Lyapunov and Floquet spectrum of
discrete-time systems. In particular we
settle an open question by presenting an example of an invariant
control set in which Lyapunov exponents may be realized that are not
contained in the closure of the Floquet spectrum corresponding to
the control set. Furthermore we show that under weak conditions the
top Lyapunov exponents behaves strictly monotone under monotone
growth of the families of time-varying systems. This implies a
strong linearization result for stability radii of nonlinear system
with respect to time-varying perturbations.


Keywords: discrete-time systems, Lyapunov exponents, controllability, stability radius