Involutive co-distributions preserved by transitive families of vector fields

Authors

  • Víctor Ayala Bravo Universidad Católica del Norte.

DOI:

https://doi.org/10.22199/S07160917.1994.0001.00006

Keywords:

Co-distributions preserved by families of vector fields, Integrability

Abstract

This paper deals with integrability conditions of involutive co-distributions defined on the co-tangent bundle of a differentiable manifold M. Via Frobeniu.s 's integrability theorem, the analysis is aimed at the search of conditions so that this type of co-distributions be preserved by transitive familiee of vector fields in M. We rely on the work of Lobry, Sussmann, Matsuda and Stefan. The type of situation studied comes up naturally in weak-observability problems and weakly- minimal realizations of arbitrary control systems.

Author Biography

Víctor Ayala Bravo, Universidad Católica del Norte.

Departamento de Matemática.

Facultad de Ciencias.

References

[1] Ayala. V. and San Martin, L., Minimal realizations under controllability,Systems Control Letters 16 ( 1991) 289-293.

[2] Ayala, V., Sobre a Observabilidade de Sistemas de Controle, Doutor em Ciencias, Thesis, Universidade Estadual de Campinas, Brasil, 1988.

[3] Basto Concalvez, J. Nonlinear observability and duality, Systems Control Letters 4 (1984) 97-101.

[4] Hermann, R. and Krener, A. Nonlinear controllability and observability, IEEE Trans. Automat. Control 22(5) (1977) 728-740.

[5] Lobry,C., Controlabilite des systemes non lineaires, SIAM J. Control 8 (1970) 573-605.

[6] Matsuda, M., An integration theorem for completely integrable systems with singularities, Osaka J. Math. 5 (1968), 279-283.

[7] Stefan, P., Accesible sets, orbits and foliations with singularities, Proc. London Math. Soc. 29 (1974) 699-713.

[8] Stefan, P., Integrability of Systems of Vector Fields, J. London Math. Vol. 2, 21 (1980).

[9] Sussmann, H., Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973) 171-188.

[10] Warner, F., Foundations of Differentiable Manifolds and Lie Groups, Scott, Foresman and Company, Glenview Illinois, 1971.

Published

2018-04-03

How to Cite

[1]
V. Ayala Bravo, “Involutive co-distributions preserved by transitive families of vector fields”, Proyecciones (Antofagasta, On line), vol. 13, no. 1, pp. 35-52, Apr. 2018.

Issue

Section

Artículos