Affine systems on Lie groups and outer invariance entropy

TL;DR

This paper investigates the outer invariance entropy of affine systems on Lie groups, revealing that it equals the sum of positive real parts of eigenvalues of a related derivation, extending linear system results.

Contribution

It extends the understanding of outer invariance entropy from linear to affine systems on Lie groups, providing a formula involving eigenvalues of a derivation.

Findings

Outer invariance entropy for affine systems equals sum of positive eigenvalue parts.

The result generalizes linear system entropy formulas to affine systems.

Eigenvalues of a derivation determine the entropy value.

Abstract

Affine systems on Lie groups are a generalization of linear systems. For such systems, this paper studies what happens with the outer invariance entropy introduced by Colonius and Kawan. It is shown that, as for linear case, the outer invariance entropy of affine systems is given by the sum of the positive real parts of the eigenvalues of a derivation D* that is associated to the drift of the system.