Global controllability properties of linear control systems

TL;DR

This paper investigates the global controllability of linear control systems by compactifying the state space with the Poincaré sphere and analyzing the induced control flow to construct invariant manifolds.

Contribution

It introduces a novel approach using the Poincaré sphere to analyze global controllability and constructs invariant manifolds for linear control systems.

Findings

Invariant manifolds are constructed on the Poincaré sphere.

The approach provides insights into the global behavior of control systems.

The method extends local controllability analysis to a global setting.

Abstract

For linear control systems with bounded control range, the state space is compactified using the Poincar\'e sphere. The linearization of the induced control flow allows the construction of invariant manifolds on the sphere and of corresponding manifolds in the state space of the linear control system.