# Invariance entropy, quasi-stationary measures and control sets

## TL;DR

This paper explores measure-theoretic invariance entropy for discrete-time control systems, demonstrating its invariance under transformations and its dependence on controllability properties of specific subsets.

## Contribution

It introduces a measure-theoretic invariance entropy framework for control systems using quasi-stationary measures, highlighting its invariance and dependence on controllability subsets.

## Key findings

- Invariance entropy remains unchanged under measurable transformations.
- Entropy is determined by controllability properties of specific subsets.
- The framework applies to control systems with probabilistic control ranges.

## Abstract

For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure. The main results show that this entropy is invariant under measurable transformations and that it is already determined by certain subsets of Q which are characterized by controllability properties.