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Alexandre Santana

Publications and source records attributed to Alexandre Santana.

5 recordsLinked to original sources
arXiv2024

Controllability of discrete-time linear systems on solvable Lie groups

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.

math.OC↗
arXiv2023

On invariant control sets for control systems on $S^3$

In this paper we describe the Lie-theoretic structure of ${\rm SO}(1,4)$ and consider control systems given by certain vector fields of ${\rm SO}(1,4)$. Then we explicitly describe its invariant control sets in the unique ${\rm SO}(1,4)$-flag manifold, namely the sphere $S^3$.

math.OC↗
arXiv2022

Controllability of periodic linear systems, the Poincare sphere, and quasi-affine systems

For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists. It is determined by the spectral subspaces of the homogeneous part which is a periodic linear differential equation. Using the Poincar\'e sphere one obtains a compactification of the state space allowing us to describe the behavior near infinity of the original control system. Furthermore, an application to quasi-affine systems yields a unique control set with nonvoid interior.

math.OC↗