Special Issue: Celebrating the 75th Birthday of V.V. Kozlov (Issue Editors: Sergey Bolotin, Vladimir Dragović, and Dmitry Treschev)

Lyapunov Exponents of Linear Switched Systems

Andrei A. Agrachev, Michele Motta

SISSA, Via Bonomea 265, 34136 Trieste, Italy

Abstract: We explicitly compute the maximal Lyapunov exponent for a switched system on $\mathrm{SL}_2(\mathbb R)$ and the corresponding switching function which realizes the maximal exponent. This computation is reduced to the characterization of optimal trajectories for an optimal control problem on the Lie group.

Keywords: control theory, optimal control, switched system, dynamical systems, Lyapunov exponents

MSC: 93D20, 34H05, 49K15

Received: 08.04.2025
Accepted: 10.07.2025

Language: English

DOI: 10.1134/S1560354725040033