Asymptotic null controllability of bilinear systems

Fritz Colonius; Wolfgang Kliemann

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 139-148
  • ISSN: 0137-6934

Abstract

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The region of asymptotic null controllability of bilinear systems with control constraints is characterized using Lyapunov exponents. It is given by the cone over the region of attraction of the maximal control set in projective space containing zero in its spectral interval.

How to cite

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Colonius, Fritz, and Kliemann, Wolfgang. "Asymptotic null controllability of bilinear systems." Banach Center Publications 32.1 (1995): 139-148. <http://eudml.org/doc/262635>.

@article{Colonius1995,
abstract = {The region of asymptotic null controllability of bilinear systems with control constraints is characterized using Lyapunov exponents. It is given by the cone over the region of attraction of the maximal control set in projective space containing zero in its spectral interval.},
author = {Colonius, Fritz, Kliemann, Wolfgang},
journal = {Banach Center Publications},
keywords = {Lyapunov exponents; asymptotically null controllability; bilinear system; time-varying},
language = {eng},
number = {1},
pages = {139-148},
title = {Asymptotic null controllability of bilinear systems},
url = {http://eudml.org/doc/262635},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Colonius, Fritz
AU - Kliemann, Wolfgang
TI - Asymptotic null controllability of bilinear systems
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 139
EP - 148
AB - The region of asymptotic null controllability of bilinear systems with control constraints is characterized using Lyapunov exponents. It is given by the cone over the region of attraction of the maximal control set in projective space containing zero in its spectral interval.
LA - eng
KW - Lyapunov exponents; asymptotically null controllability; bilinear system; time-varying
UR - http://eudml.org/doc/262635
ER -

References

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  3. [3] B. F. Bylov, R. E. Vinograd, D. M. Grobman, V. V. Nemytskiĭ, Theory of Lyapunov Exponents, Nauka, Moscow, 1966 (in Russian). 
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  5. [5] R. Chabour, G. Sallet and J. C. Vivalda, Stabilization of nonlinear systems: a bilinear approach, Math. Control Syst. Signals (1993), to appear. Zbl0797.93038
  6. [6] F. Colonius and W. Kliemann, Infinite time optimal control and periodicity, Appl. Math. Optim. 20 (1989), 113-130. Zbl0685.49002
  7. [7] F. Colonius and W. Kliemann, Maximal and minimal Lyapunov exponents of bilinear control, J. Differential Equations 101 (1993), 232-275. Zbl0769.34037
  8. [8] F. Colonius and W. Kliemann, Linear control semigroups acting on projective space, J. Dynamics Differential Equations 5 (1993), 495-528. Zbl0784.34049
  9. [9] F. Colonius and W. Kliemann, Controllability and stabilization of one dimensional systems, Systems Control Lett. 24 (1995), 87-95. Zbl0877.93091
  10. [10] F. Colonius and W. Kliemann, The Morse spectrum of linear flows on vector bundles, Trans. Amer. Math. Soc. (1995), to appear. Zbl0864.58051
  11. [11] F. Colonius and W. Kliemann, The Lyapunov spectrum of families of time-varying matrices, Trans. Amer. Math. Soc. (1995), to appear. Zbl0873.93054
  12. [12] J. P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57 (1985), 617-656. Zbl0989.37516
  13. [13] J. P. Gauthier, I. Kupka and G. Sallet, Controllability of right invariant systems on real semi simple Lie groups, Systems Control Lett. 5 (1984), 187-190. Zbl0552.93010
  14. [14] W. Hahn, The Stability of Motion, Springer, 1967. Zbl0189.38503
  15. [15] E. C. Joseph, Stability radii of two dimensional bilinear systems, Ph. D. Thesis, Department of Mathematics, Iowa State, 1993. 
  16. [16] A. M. Lyapunov, Problème générale de la stabilité du mouvement, Comm. Soc. Math. Kharkov 2 (1892). 
  17. [17] V. I. Oseledeč, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc 19 (1968), 197-231. 
  18. [18] E. D. Sontag, Feedback stabilization of nonlinear systems, in: Robust Control of Linear Systems and Nonlinear Control, M. A. Kashoek, J. H. van Schuppen, A. C. Ran (eds.), Birkhäuser, 1990, 61-81. Zbl0735.93063

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