Controllability of discrete-time linear systems on solvable Lie groups

TL;DR

This paper investigates the controllability of discrete-time linear systems on solvable Lie groups, providing necessary and sufficient conditions in specific cases like nilpotent and affine Lie groups.

Contribution

It establishes controllability criteria for discrete-time linear systems on solvable Lie groups, including nilpotent and affine cases, advancing understanding in geometric control theory.

Findings

Controllability condition for nilpotent Lie groups

Controllability criteria for affine Lie group systems

Characterization of controllability in solvable Lie groups

Abstract

The objective of this paper is to study the controllability of discrete-time linear control systems in solvable Lie groups. In the special case of nilpotent Lie groups, a necessary and sufficient condition for controllability is established. Furthermore, the class of discrete-time linear systems in the two-dimensional affine Lie group is constructed and a condition for controllability of these systems is also stated.