activity
20142024
most citedAlmost-Riemannian Structures on nonnilpotent, solvable 3D Lie groups

4 citations · 14 across the 18 of their papers we have counts for

collaborators

22 papers

math.OC2024

Control sets of linear control systems on . The real case

Victor Ayala, Adriano Da Silva, Anderson F. P. Rojas

In this paper, we study the dynamical behavior of a linear control system on when the associated matrix has real eigenvalues. Different from the complex case, we show that t…

math.OC2024

One-input linear control systems on the homogeneous spaces of the Heisenberg group -- The singular case

Adriano Da Silva, Okan Duman, Eyüp Kizil

The controllability issue of control-affine systems on smooth manifolds is one of the main problems in the theory, and it is recently known [Jouan P. Equivalence of control systems…

math.OC2023

Weak condition for the existence of control sets with a nonempty interior of linear control systems on nilpotent groups

Adriano Da Silva, Anderson Felipe Penagos Rojas

In this paper, we show that for a linear control system on a nilpotent Lie group, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty…

math.OC2023

Control sets of one-input linear control systems on solvable, nonnilpotent 3D Lie groups

Adriano Da Silva, Lino Grama, Alejandro Otero Robles

In this article, we completely describe the control sets of one-input linear control systems on solvable, nonnilpotent 3D Lie groups. We show that, if the restriction of the associ…

math.DG2023

Isometries of Almost-Riemannian structures on nonnilpotent, solvable 3D Lie groups

Victor Ayala, Adriano Da Silva, Danilo A. Garcia Hernández

In this paper we prove that automorphisms are the only isometries between rank two Almost-Riemannian Structures on the class of nonnilpotent, solvable, connected 3D Lie groups. As…

math.OC2023★ 1 cited

The chain control set of a linear control system

Adriano Da Silva

In this paper, we analyze the chain control sets of linear control systems on connected Lie groups. Our main result shows that the compactness of the central subgroup associated wi…

math.OC2023★ 1 cited

Minimal-time trajectories of a linear control system on a homogeneous space of the 2D Lie group

Victor Ayala, Adriano Da Silva, Maria Torreblanca

Through the Pontryagin maximum principle, we solve a minimal-time problem for a linear control system on a cylinder, considered as a homogeneous space of the solvable Lie group of…

math.OC2022

Control sets of linear control systems on . The complex case

Victor Ayala, Adriano Da Silva, Erik Mamani

This paper explicitly computes the unique control set with non-empty interior of a linear control system on , when the associated matrix has complex eigenvalues.…

math.OC2022★ 4 cited

Almost-Riemannian Structures on nonnilpotent, solvable 3D Lie groups

Victor Ayala, Danilo A. García Hernández, Adriano Da Silva

In this paper we study Almost-Riemannian Structures (ARS) on the class of nonnilpotent, solvable, conneted 3D Lie groups. The nice structures present in such groups allow us to sho…

math.OC2020

On the structural properties of the bounded control set of a linear control system

Victor Ayala, Adriano Da Silva

The present paper shows that the bounded control set of a linear system on a connected Lie group contains all the bounded orbits of the system. As a consequence, its closure is…

math.OC2017

Invariance entropy for a class of partially hyperbolic sets

Christoph Kawan, Adriano Da Silva

Invariance entropy is a measure for the smallest data rate in a noiseless digital channel above which a controller that only receives state information through this channel is able…

math.OC2016

Robustness of critical bit rates for practical stabilization of networked control systems

Adriano Da Silva, Christoph Kawan

In this paper we address the question of robustness of critical bit rates for the stabilization of networked control systems over digital communication channels. For a deterministi…

math.DS2016★ 2 cited

Continuity of reachable sets of restricted affine control systems

Victor Ayala, Adriano Da Silva

In this paper we give a direct proof that for a restricted affine control system on a connected manilfold M, the associated reachable sets up to time t varies continuously with the…

math.DS2016

Topological entropy of a Lie group automorphism

Victor Ayala, Adriano Da Silva, Heriberto Román-Flores

Let ϕ be an automorphism on a connected Lie group G. Through several G-subgroups associated to the dynamics of ϕ we analyze their topological entropy. Assume that G belongs to the…

math.DS2016

Topological conjugacy of linear systems on Lie groups

A. Da Silva, A. J. Santana, S. N. Stelmastchuk

In this paper we study a classification of linear systems on Lie groups with respect to the conjugacy of the corresponding flows. We also describe stability according to Lyapunov e…

math.DS2016

Control Systems on Flag Manifolds and their chain Control sets

Victor Ayala, Adriano Da Silva, Luiz A. B. San Martin

In this paper we shown that the chain control sets of induced systems on flag manifolds coincides with their analogous one defined via semigroup actions. Consequently, any chain co…

math.OC2016★ 3 cited

Controllability of linear systems on Lie groups with finite semisimple center

Adriano Da Silva, Victor Ayala

In this paper we extend the results on controllability of linear systems obtained in "Controllability of linear systems on solvable Lie groups", from solvable Lie groups to Lie gro…

math.OC2015

Affine systems on Lie groups and outer invariance entropy

Adriano Da Silva

Affine systems on Lie groups are a generalization of linear systems. For such systems, this paper studies what happens with the outer invariance entropy introduced by Colonius and…

math.DS2014

Control sets of linear systems on Lie groups

Adriano Da Silva, Victor Ayala, Guilherme Zsigmond

Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies the properties of the maximal sets of approxima…

math.OC2014

Controllability of linear systems on solvable Lie groups

Adriano Da Silva

Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies controllability by taking in consideration the…

math.OC2014

Invariance Entropy of Hyperbolic Control Sets

Adriano Da Silva, Christoph Kawan

In this paper, we improve the known estimates for the invariance entropy of a nonlinear control system. For sets of complete approximate controllability we derive an upper bound in…

math.OC2014★ 3 cited

Hyperbolic Chain Control Sets on Flag Manifolds

Adriano Da Silva, Christoph Kawan

In this paper we study the chain control sets of right-invariant control systems on the flag manifolds of a non-compact semisimple Lie group. We prove that each chain control set i…