Outer invariance entropy for discrete-time linear systems on Lie groups

TL;DR

This paper studies the outer invariance entropy of discrete-time linear control systems on Lie groups, providing bounds and conditions under which the bounds are tight, advancing understanding of control complexity on these mathematical structures.

Contribution

It introduces a new framework for analyzing invariance entropy on Lie groups and establishes conditions for exact entropy calculation.

Findings

Upper bound for outer invariance entropy derived

Equality of bounds established under specific conditions

Conditions involving the stable subgroup and measure are identified

Abstract

We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs (K,Q). If the stable subgroup of the uncontrolled system is closed and K has positive measure for a left invariant Haar measure, the upper bound coincides with the outer invariance entropy.