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## Banach Center Publications

1995 | 32 | 1 | 35-46
Tytuł artykułu

### Controllability of nilpotent systems

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we study the controllability property of invariant control systems on Lie groups. In [1], the authors state: If there exists a real function strictly increasing on the positive trajectories, then the system cannot be controllable". To develop this idea, the authors define the concept of symplectic vector via the co-adjoint representation. We are interested in finding algebraic conditions to determine the existence of symplectic vectors in nilpotent Lie algebras. In particular, we state a necessary and sufficient condition for controllability in the simply connected nilpotent case.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
35-46
Opis fizyczny
Daty
wydano
1995
Twórcy
autor
• Departamento de Matemática, Universidad Católica del Norte Casilla, 1280, Antofagasta, Chile
Bibliografia
• [1] V. Ayala and L. Vergara, Co-adjoint representation and controllability, Proyecciones 11 (1992), 37-48.
• [2] B. Bonnard, V. Jurdjevic, I. Kupka and G. Sallet, Transitivity of invariant vector fields on the semidirect product of Lie groups, Trans. Amer. Math. Soc. 271 (1982), 521-535.
• [3] R. Brockett, Systems theory on group manifolds and coset spaces, SIAM J. Control 10 (1972), 265-284.
• [4] L. Corwin and F. Greenleaf, Representations of Nilpotent Lie Groups and Their Applications, Part I, Cambridge University Press, 1990.
• [5] V. Jurdjevic and I. Kupka, Control systems on semi-simple Lie groups and their homogeneous spaces, Ann. Inst. Fourier (Grenoble) 31 (4) (1981), 151-179.
• [6] V. Jurdjevic and H. Sussmann, Control systems on Lie groups, J. Differential Equations 12 (1972), 313-329.
• [7] I. Kupka, Introduction to the Theory of Systems, 16 Coloquio Brasileiro de Matematica, 1987.
• [8] L. San Martin and P. Crouch, Controllability on principal fibre bundle with compact structure group, Systems Control Letters 5 (1984), 35-40.
• [9] H. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171-188.
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