Related papers: Existence and uniqueness of control sets with a no…
Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. When the state space is a solvable connected Lie group, controllability of the linear system is assured if the ad-rank condition holds.
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 set of a hyperbolic linear control system in R^{d} this yields…
In this paper, we investigate the control sets of linear control systems on the Heisenberg group associated with singular derivations. Under the Lie algebra rank condition, we provide a complete characterization of these sets by analyzing…
This paper presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group, the special linear group and the general linear group, respectively, in the presence of drift…
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 groups with finite semisimple center.
In control theory, researchers need to understand a system's local and global behaviors in relation to its initial conditions. When discussing observability, the main focus is on the ability to analyze the system using an output space…
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 classical Diophantine approximation result. For affine control…
For bilinear control systems in $\mathbb{R}^d$ we prove, under an accessibility hypothesis, the existence of a nontrivial compact set $D\subset\mathbb{R}^d$ satisfying $\mathcal{O}_t(D)=e^{tR}D$ for all $t>0$, where $R\in\mathbb{R}$ is a…
The controllability condition for finite dimensional quantum systems, the Lie Algebra Rank Condition, has been stated assuming that the right invariant differential system under consideration is bilinear. We remark that this assumption is…
We prove the existence of a universal gap for minimum time controllability of finite dimensional quantum systems, except for some basic representations of spin groups. This is equivalent to the existence of a gap in the diameter of orbit…
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 given basically by the product of the exponential of the…
This paper studies controllability of a discrete-time linear dynamical system using nonnegative and sparse inputs. These constraints on the control input arise naturally in many real-life systems where the external influence on the system…
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 control set of the system contains a control set with nonempty…
In this paper we study affine and bilinear systems on Lie groups. We show that there is an intrinsic connection between the solutions of both systems. Such relation allows us to obtain some preliminary controllability results of affne…
Let $S$ be subsemigroup with nonempty interior of a complex simple Lie group $G$. It is proved that $S=G$ if $S$ contains a subgroup $G(\alpha) \approx \mathrm{Sl}(2,\mathbb{C}) $ generated by the $\exp \mathfrak{g}_{\pm \alpha}$, where…
The local controllability of a rich class of affine nonlinear control systems with nonhomogeneous quadratic drift and constant control vector fields is analyzed. The interest in this particular class of systems stems from the ubiquity in…
In this work, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on the input arises naturally in networked systems, where activating each input variable adds to the…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
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. For hyperbolic systems there is a unique control set with…
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 the sum of the control set around the origin and the center…