Fabian Wirth
On Lipschitz continuity of the top Lyapunov exponent of linear parameter varying and linear switching systems.
Preprint series:
MSC:
37C60
34C11,34D10
Abstract:
We study families of time-varying linear systems, where time-variations have to satisfy restrictions on the dwell time, that is, on the minimum distance between discontinuities, as well as on the derivative in between discontinuities. For this class of systems we study continuity properties of the growth rate as a function of the systems' data. It is shown by example, that a straightforward topology on the space of systems does not yield the desired continuity result. A new natural metric is introduced and a continuity result is obtained. Furthermore, local Lipschitz continuity may be shown for the (generic) case of irreducible systems. The methods rely heavily on a recent converse Lyapunov theorem for the class under consideration.

Keywords: converse Lyapunov theorem, linear parameter varying systems, linear switching systems, linear flows on vector bundles, growth rate, Lipschitz continuity, parameterized Lyapunov function.

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Home Fabian Wirth's publication page Research Group "Regelungssysteme"
Zentrum für Technomathematik (German)
Institute for Dynamical Systems
The Maths Department
The University of Bremen

Notes:
accepted for publication by Stochastics & Dynamics