Invariant cones for semigroups and controllability of bilinear control systems

TL;DR

This paper establishes necessary and sufficient conditions for the existence of invariant cones under semigroup actions and applies these results to determine controllability conditions for certain bilinear control systems.

Contribution

It introduces a new criterion for invariant cones in the space of exterior products and links this to controllability of bilinear systems.

Findings

Invariant cones characterized by new conditions

Controllability criteria derived for specific bilinear systems

Theoretical framework connecting invariant cones and control properties

Abstract

In this paper we present necessary and sufficient conditions to guarantee the existence of invariant cones, for semigroup actions, in the space of the $k$-fold exterior product. As consequence we establish a necessary and sufficient condition for controllability of a class of bilinear control systems.