21 citations · 71 across the 19 of their papers we have counts for
22 papers
Global controllability properties of linear control systems
Fritz Colonius, Alexandre J. Santana
For linear control systems with bounded control range, the state space is compactified using the Poincaré sphere. The linearization of the induced control flow allows the construct…
Strong chain control sets and affine control systems
Fritz Colonius, Alexandre J. Santana
For control-affine systems on non-compact manifolds, the notion of strong chain control sets is introduced and related to the strong chain transitivity of the associated control fl…
Chain controllability of linear control systems
Fritz Colonius, Alexandre J. Santana, Eduardo C. Viscovini
For linear control systems with bounded control range, chain controllability properties are analyzed. It is shown that there exists a unique chain control set and that it equals th…
Controllability of discrete-time linear systems on lie groups with finite semisimple center
Thiago Cavalheiro, Alexandre Santana, João Cossich
In this paper we stated a condition for the controllability of discrete-time linear systems for the case when the Lie group has finite semisimple center and provided a example in t…
Chain recurrence and Selgrade`s theorem for affine flows
Fritz Colonius, Alexandre J. Santana
Affine flows on vector bundles with chain transitive base flow are lifted to linear flows and the decomposition into exponentially separated subbundles provided by Selgrade's theor…
Controllability of discrete-time linear systems on solvable Lie groups
Thiago Cavalheiro, Alexandre Santana, João Cossich +1
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…
Controllability of periodic linear systems, the Poincare sphere, and quasi-affine systems
Fritz Colonius, Alexandre Santana, Juliana Setti
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.,…
Control Sets for Affine Systems, Spectral Properties and Projective Spaces
Fritz Colonius, Alexandre J. Santana, Juliana Setti
For affine control systems with bounded control range the control sets, i.e., the maximal subsets of complete approximate controllability, are studied using spectral properties. Fo…
Invariant cones for semigroups and controllability of bilinear control systems
Emerson V. Castelani, João A. N. Cossich, Alexandre J. Santana +1
In this paper we present necessary and sufficient conditions to guarantee the existence of invariant cones, for semigroup actions, in the space of the -fold exterior product. As…
Control Sets for Bilinear and Affine Systems
Fritz Colonius, Juliana Raupp, Alexandre J. Santana
For homogeneous bilinear control systems, the control sets are characterized using a Lie algebra rank condition for the induced systems on projective space. This is based on a clas…
Semigroups and Controllability of Invariant Control Systems on
Bruno A. Rodrigues, Luiz A. B. San Martin, Alexandre J. Santana
Let be the Lie group of quaternionic matrices with . We prove that a subsemigroup $S \subse…
Outer invariance entropy for discrete-time linear systems on Lie groups
Fritz Colonius, João A. N. Cossich, Alexandre J. Santana
We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs (K,Q). If the stable subgr…
The General Solution for Affine Control Systems on Lie Groups
João Paulo Lima de Oliveira, Alexandre José Santana, Simão Nicolau Stelmastchuk
The purpose of this paper is to present explicitly the solution curve for affine control systems on Lie groups under the assumption that automorphisms associated to the linear vect…
Solution Curve for Linear Control Systems on Lie Groups
João Paulo Lima de Oliveira, Alexandre J. Santana, Simão N. Stelmastchuk
The purpose of this paper is to describe explicitly the solution for linear control systems on Lie groups. In case of linear control systems with inner derivations, the solution is…
Controllability properties and invariance pressure for linear discrete-time systems
Fritz Colonius, João A. N. Cossich, Alexandre J. Santana
For linear control systems in discrete time controllability properties are characterized. In particular, a unique control set with nonvoid interior exists and it is bounded in the…
Bounds for Invariance Pressure
Fritz Colonius, Alexandre J. Santana, João A. N. Cossich
This paper provides an upper for the invariance pressure of control sets with nonempty interior and a lower bound for sets with finite volume. In the special case of the control se…
Invariance pressure of control sets
Fritz Colonius, João A. N. Cossich, Alexandre J. Santana
The invariance pressure of continuous-time control systems with initial states in a set K which are to be kept in a set Q is introduced and a number of results are derived, mainly…
Invariance Pressure for Control Systems
Fritz Colonius, Alexandre J. Santana, João A. N. Cossich
Notions of invariance pressure for control systems are introduced based on weights for the control values. The equivalence is shown between inner invariance pressure based on spann…
Orbit equivalence of linear systems on manifolds and semigroup actions on homogeneous spaces
Rafael M. Hungaro, Osvaldo G. Rocio, Alexandre J. Santana
In this paper we introduce the notion of orbit equivalence for semigroup actions and the concept of generalized linear control system on smooth manifold. The main goal is to prove…
A topological conjugacy of invariant flows on some class of Lie groups
Alexandre J. Santana, Simão N. Stelmastchuk
The aim of this paper is to give a condition to topological conjugacy of invariant flows in an Lie group which its Lie algebra is associative algebra or semisimp…
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…
Harmonic Maps into Homogeneous Spaces According to a Darboux Homogeneous Derivative
Alexandre J. Santana, Simão N. Stelmastchuk
Our purpose is to use a Darboux homogenous derivative to understand the harmonic maps with values in homogeneous space. We present a characterization of these harmonic maps from th…