# Invariance Pressure for Control Systems

## TL;DR

This paper introduces the concept of invariance pressure for control systems, establishing its theoretical foundations, properties, and computation methods for linear systems, enhancing understanding of control invariance measures.

## Contribution

It defines invariance pressure using control weights, proves equivalence between different formulations, and computes it for linear systems, advancing control theory.

## Key findings

- Invariance pressure is equivalent when based on spanning sets or invariant open covers.
- Properties of invariance pressure are systematically derived.
- Invariance pressure is explicitly computed for a class of linear systems.

## Abstract

Notions of invariance pressure for control systems are introduced based on weights for the control values. The equivalence is shown between inner invariance pressure based on spanning sets of controls and on invariant open covers, respectively. Furthermore, a number of properties of invariance pressure are derived and it is computed for a class of linear systems.