On the gap between deterministic and probabilistic Lyapunov exponents for continuous-time linear systems
Optimization and Control
2023-03-21 v2 Dynamical Systems
Probability
Abstract
Consider a non-autonomous continuous-time linear system in which the time-dependent matrix determining the dynamics is piecewise constant and takes finitely many values . This paper studies the equality cases between the maximal Lyapunov exponent associated with the set of matrices , on the one hand, and the corresponding ones for piecewise deterministic Markov processes with modes , on the other hand. A fundamental step in this study consists in establishing a result of independent interest, namely, that any sequence of Markov processes associated with the matrices converges, up to extracting a subsequence, to a Markov process associated with a suitable convex combination of those matrices.
Cite
@article{arxiv.2112.07005,
title = {On the gap between deterministic and probabilistic Lyapunov exponents for continuous-time linear systems},
author = {Yacine Chitour and Guilherme Mazanti and Pierre Monmarché and Mario Sigalotti},
journal= {arXiv preprint arXiv:2112.07005},
year = {2023}
}