Related papers: A necessary and sufficient condition for local con…

This note is concerned with the stability and stabilization of the linearized spacecraft attitude control system. Necessary and sufficient conditions are respectively provided to guarantee that the considered systems are polynomially stable…

Solutions of a system of wave equations are constructed for both homogeneous and inhomogeneous Dirichlet boundary conditions at every regularity level. We prove that boundary observability, and thus boundary exact controllability, at some…

We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the orbit closure of the permanent multiplied by a power of a linear form.

We give new computable necessary conditions for a class of optimal transportation problems to have smooth solutions.

In this work we study homeomorphisms of closed orientable surfaces homotopic to the identity, focusing on the existence of non-contractible periodic orbits. We show that, if $g$ is such a homeomorphism, and if $\hat g$ is its lift to the…

We give necessary and sufficient conditions for an operator on a separable Hilbert space to satisfy the hypercyclicity criterion.

We consider in this paper the regularity problem for time-optimal trajectories of a single-input control-affine system on a n-dimensional manifold. We prove that, under generic conditions on the drift and the controlled vector field, any…

The case of time minimization for affine control systems with control on the disk is studied. After recalling the standard sufficient conditions for local optimality in the smooth case, the analysis focusses on the specific type of…

By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…

A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General…

In this paper we extend the work in the conference paper 'On the Controllability and Observability of Heterogeneous Networked Systems with distinct node dimensions and inner-coupling matrices' wherein the controllability and observability…

Let $M$ be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian $H:T^*M\rightarrow \mathbb R$ and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits…

We give a necessary condition that a separable measurement can be implemented by local quantum operations and classical communication (LOCC) in any finite number of rounds of communication, generalizing and strengthening a result obtained…

In this paper, we obtain an analogue of the discrete Calderon condition and prove that this condition is sufficient for an orthonormal twisted wavelet system to be complete in L^{2}(R^{2}).

We show that the orbit closures for directing modules over tame algebras are normal and Cohen-Macaulay. The proof is based on deformations to normal toric varieties.

It is very well known that periodic orbits of autonomous Hamiltonian systems are generically organized into smooth one-parameter families (the parameter being just the energy value). We present a simple example of an integrable Hamiltonian…

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…

Given two elements of a vector space acted on by a reductive group, we ask whether they lie in the same orbit, and if not, whether one lies in the orbit closure of the other. We develop techniques to optimize the orbit and orbit closure…

The celebrated geometric control condition of Bardos, Lebeau, and Rauch is necessary and sufficient for wave observability [1,7] and exact controllability. It requires that any point in phase-space be transported by the generalized geodesic…

Let $(M,g)$ be a closed Riemannian manifold and $L:TM\rightarrow \mathbb R$ be a Tonelli Lagrangian. In this thesis we study the existence of orbits of the Euler-Lagrange flow associated with $L$ satisfying suitable boundary conditions. We…