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