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We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let X and Y be two smooth vector fields on a two-dimensional manifold M . If X and Y areâ€¦ (More)

- IN R, Andrei A. Agrachev, Mario Sigalotti
- 2003

We analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system qÌ‡ = f(q) + u g(q) in a three-dimensional manifold, near a point where some nondegeneracyâ€¦ (More)

The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form aâ€¦ (More)

- Pierre Riedinger, Mario Sigalotti, Jamal Daafouz
- Automatica
- 2010

In this paper, a suitable LaSalle principle for continuous-time linear switched systems is used to characterize invariant sets and their associated switching laws. An algorithm to determineâ€¦ (More)

- Andrei A. Agrachev, Ugo V. Boscain, Gregoire Charlot, Roberta Ghezzi, Mario Sigalotti
- Proceedings of the 48h IEEE Conference onâ€¦
- 2009

Two dimensional almost-Riemannian geometries are metric structures on surfaces defined locally by a Lie bracket generating pair of vector fields. We study the relation between the topology of anâ€¦ (More)

We prove approximate controllability of the bilinear SchrÃ¶dinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant spectrum. The results that are obtained apply bothâ€¦ (More)

- Ugo V. Boscain, Marco Caponigro, Thomas Chambrion, Mario Sigalotti
- ArXiv
- 2011

In this paper we prove an approximate controllability result for the bilinear SchrÃ¶dinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolledâ€¦ (More)

- Ð³. A. Braides, M Gelli, Mario Sigalotti
- 2009

We treat the problem of the description of the limits of discrete variational problems with long-range interactions in a one-dimensional setting. Under some polynomial-growth condition on the energyâ€¦ (More)

In [16] we proposed a set of sufficient conditions for the approximate controllability of a discrete-spectrum bilinear SchrÃ¶dinger equation. These conditions are expressed in terms of the controlledâ€¦ (More)

Consider the controlled system dx/dt = Ax + Î±(t)Bu where the pair (A,B) is stabilizable and Î±(t) takes values in [0, 1] and is persistently exciting, i.e., there exist two positive constants Î¼, Tâ€¦ (More)