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1995 | 32 | 1 | 139-148
Tytuł artykułu

Asymptotic null controllability of bilinear systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
32
Numer
1
Strony
139-148
Opis fizyczny
Daty
wydano
1995
Twórcy
  • Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany
  • Department of Mathematics, Iowa State University, Ames, Iowa 50011, U.S.A.
Bibliografia
  • [1] L. Arnold, H. Crauel and J.-P. Eckmann (eds.), Lyapunov Exponents, Lecture Notes in Math. 1486, Springer, 1991.
  • [2] L. Arnold and V. Wihstutz, Lyapunov Exponents, Lecture Notes in Math. 1186, Springer, 1986.
  • [3] B. F. Bylov, R. E. Vinograd, D. M. Grobman, V. V. Nemytskiĭ, Theory of Lyapunov Exponents, Nauka, Moscow, 1966 (in Russian).
  • [4] L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, 3rd ed., Springer, 1971.
  • [5] R. Chabour, G. Sallet and J. C. Vivalda, Stabilization of nonlinear systems: a bilinear approach, Math. Control Syst. Signals (1993), to appear.
  • [6] F. Colonius and W. Kliemann, Infinite time optimal control and periodicity, Appl. Math. Optim. 20 (1989), 113-130.
  • [7] F. Colonius and W. Kliemann, Maximal and minimal Lyapunov exponents of bilinear control, J. Differential Equations 101 (1993), 232-275.
  • [8] F. Colonius and W. Kliemann, Linear control semigroups acting on projective space, J. Dynamics Differential Equations 5 (1993), 495-528.
  • [9] F. Colonius and W. Kliemann, Controllability and stabilization of one dimensional systems, Systems Control Lett. 24 (1995), 87-95.
  • [10] F. Colonius and W. Kliemann, The Morse spectrum of linear flows on vector bundles, Trans. Amer. Math. Soc. (1995), to appear.
  • [11] F. Colonius and W. Kliemann, The Lyapunov spectrum of families of time-varying matrices, Trans. Amer. Math. Soc. (1995), to appear.
  • [12] J. P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57 (1985), 617-656.
  • [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.
  • [14] W. Hahn, The Stability of Motion, Springer, 1967.
  • [15] E. C. Joseph, Stability radii of two dimensional bilinear systems, Ph. D. Thesis, Department of Mathematics, Iowa State, 1993.
  • [16] A. M. Lyapunov, Problème générale de la stabilité du mouvement, Comm. Soc. Math. Kharkov 2 (1892).
  • [17] V. I. Oseledeč, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc 19 (1968), 197-231.
  • [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.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv32z1p139bwm
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